Chef John's Prime Rib Gravy

I loved this so much I wanted to make sure I always had the recipe available. The original recipe can be found here.

Ingredients for the Beef stock:
1 teaspoon butter for greasing pan
½ onion, unpeeled, sliced
½ cup roughly chopped carrots
½ cup roughly chopped celery
2 beef rib bones
4 cups beef bone broth or high quality, low-sodium beef broth
2 cups water

Ingredients for the Gravy:
2 tablespoons unsalted butter
1 cup sliced brown mushroom (Optional)
2 tablespoons reserved beef fat
⅓ cup all-purpose flour
3 ½ cups reserved beef stock
1 teaspoon kosher salt, or to taste
Freshly ground black pepper to taste
Cayenne to taste
1 teaspoon balsamic vinegar

Make magic:

1.    Preheat an oven to 450 degrees F (230 degrees C). Line a baking sheet with foil.

2.    Spread out onions, carrots, and celery on the prepared baking sheet. Set rib bones on top.

3.    Roast until bones are deep brown and onions are black, about 1 hour. Use a spatula or tongues to transfer bones and vegetables into a saucepan. Drain off and reserve any rendered fat from the baking sheet for the gravy.

4.    Add broth and water to the saucepan, and bring to a boil on high heat. Reduce heat to low and simmer until meat falls off bone and is flavorless, about 4 hours. Skim any fat from the surface and reserve. Strain broth and let cool to room temp.

5.    Melt butter in a pot on medium-high and sauté mushrooms until well browned. Add 2 tablespoons rendered beef fat and stir until melted. Add flour and cook for a few minutes. Whisk in broth, and bring to a simmer. Cook, stirring occasionally, about 5 minutes. Reduce heat to medium and simmer until gravy has thickened to desired thickness, 5 to 10 minutes more

6.    Adjust salt to taste and season with freshly ground black pepper, cayenne, and balsamic vinegar. Taste again, adjust, and serve.