Serf of the Mountain - Epic Fantasy

This first page really has a great deal of tension, and that's great. I got confused in some of the elements because you introduced many of them by name rather than by what those things were. It doesn't take a ton of "stage directing" to paint a picture of what's going on, but that's my personal preference. I like to know that there are people in a room before they talk, etc. (unless those words are meant to be surprising). I do think the previous comment has some excellent points.
I did have one nitpick that really drew me out of the story: I'm confused about the spears glittering with lava from beyond the shallow ridge. Is this a reference to a portal, or are they dipping their spears in lava? In which case, glitter doesn't seem like the right word. Lava doesn't typically glitter. It's most commonly sullen and red, and the consistency of honey (if it's red enough to glow), which makes it a terrible thing to dip spears into.
I don't wonder if you are trying to give us too much of your world in one go round. It might serve you better to let this page breathe a little and give us some of these details so your reader feels more grounded.
And just to be clear, it's really good as is, these are just my thoughts for improvement. Good luck!

Hey You read my first 250 words and I wanted to return the favor. I sincerely hope my comments are helpful. Just remember, our comments are suggestions only - always listen to your heart when deciding if a piece needs revisions. I mean, all our thoughts are based on our own reading style/preferences, so what each critiquer may think could vary wildly from the rest of the world.
Overall Comments/Good Questions the work left me with:
I get an impression of the setting you’re hoping for. What I suggest is to flush out this new description of world & stage you’re presenting to the reader, and give a Deep POV from your main character to show the reader how this scenario is affecting him emotionally and the physical responses he has as a reaction to his emotions.

I may paste excerpts from your work below and will comment using [CDH - ]

Tonight was the night I would put an innocent man to death.
[CDH – I like the foreshadowing of what is to come
]
“Death by ash, or by ice?” Elías Adriann asked, standing over the convict on a granite stage.
[CDH – having read the rest, intro him as Magnate Elias Adriann.
I’d like a flushed out setting here with a Deep Point of View (POV) so I get a feel for what emotions your important characters are feeling & the physical responses they have to those emotions. For example, if the convict somehow escapes and will become a main char, give me a description of him and a Deep POV. Is he a large man, is he cowering on the cold stage, is his chin raised and shoulders squared in defiance, etc. SHOW me how he feels.
]
It was impossible to find a resemblance between Elías Adriann and the cowering prisoner; without knowledge of the scandal, no one would have guessed they were cousins.
[CDH – you show him cowering here, but you need his physical reactions to the situation when you introduce him. If it’s his brother or cousin, maybe Elias leans down and growls ‘brother’ or ‘cousin’ menacingly at the prisoner. Some spat of words to show if Elias is disappointed/angry, or gentle words to show he is remorseful for what is transpiring. This is a great opportunity to SHOW the reader how these 2 feel about each other in this moment.
]
Brian Adriann—the magnate’s own blood, now tasked with deciding the means of his execution—only shivered in response.
[CDH – this is a bit confusing. It’s good information but its jammed together and didn’t help me understand. I don’t know who the magnate is, or why this blood connection would be important – if it matters, flush it out before you get here so the reader knows its importance. You could consider revising to be something like: Brian Adriann, now expected to decide the means of his own execution, responded with a sob/whine and a shiver.
]
Flakes of ice crusted his beard, and hypothermia had left his extremities black and gnarled like overcooked meat. A starry sky illuminated pockets of prison cells at the top of the chasm, where Brian had roomed for the past week.
[CDH – I do feel the data is important, but the way it’s presented could flow smoother. Maybe his eyes cast upward for the briefest of seconds to find the window belonging to the room that had imprisoned him for the past week. A starry sky illuminated pockets of prison cells at the top of the chasm. His lip trembled, and he hung his head. Or...maybe he chances a look up at Elias and a tear trails down his face. Then, Elias could react.
The link of hypothermia to cooked meat didn’t resonate well – the image didn’t form properly in my mind. Maybe a desc something like: his blackened limbs, shriveled and useless, resembled a deer’s carcass discarded in the snow all winter.
I’m trying to give examples of a way you could break out important data that’s been crammed too close together. Sometimes, that gets clunky and your wonderful story won’t evoke the emotions and images you’ve meant your reader to experience.
]
Augustins called it The Lid. Weeks of malnutrition up there, so close to the sink hole’s lip, had turned him into a memory of his old self.
[CDH – Again, if the prisoner becomes pertinent to the story at a later time by being alive and active in the book’s journey – then it’s important for the reader to know a lot of information about him. If he’s just going to die, you can give a Deep POV from one of his living relatives or friends now or later so the reader feels the impact of his death and how it affected others.
]
“Death by ash, or death by ice?” Magnate Elías repeated. He twisted the ring on his forefinger, expression grim, as if taking no pleasure in the trial.
Brian whimpered.
[CDH – Don’t tell the reader what you assume the char to feel (taking no pleasure in it) – stick to giving physical responses to the scenario to show his emotions. Like: Elias’ skin paled/greyed, an unpleasant/dire expression crossed his face, and he fidgeted with the ring on his forefinger. == SHOW how he’s feeling.
I suggest entering to a new line to go from 1 char to another. So, Elias gets his own sentence/paragraph, and when a new character (Brian) or stimulus is presented, it gets their own sentence/paragraph. Keeping the readers separate helps the reader keep track of who is saying and doing what.
]
Every sound that escaped his throat summoned vivid images of how I would kill him. Would he care if I had no choice in the matter? Of course not. Mole rats didn’t care who held the knife during their slaughter. But what about the people crowding the street, intently watching the trial? Would they be capable of sympathy?
[CDH – Every sound that escaped who’s throat? Maybe say every sound that escaped Brian summoned gruesome/unwarranted images of how I’d have to kill him. I’m guessing how Elias feels because I don’t have a good grip on if he wants to do it or is very reluctant at this point.
Maybe ask ‘will he forgive me for having no choice in the manner’ – this would show Elias is holding on to some hope he will be forgiven. Then he could grunt or sneer and think ‘of course not…rats didn’t care who killed them or why, all they know is the blade slicing their throat.
If Elias is hoping the crowd will be kinder, more compassionate to his plight as his family’s executioner, I’d say this is a great place to describe that. Maybe he scans the people looking for understanding eyes or body language. Then have him react to whatever he finds in their faces – maybe he scoffs if they don’t seem understanding, or he gives a tiny nod to someone who offers him an understanding smile.
]