Step 1
Season the elk filet mignon generously with salt and black pepper.

Step 2
Heat avocado oil in a heavy skillet over medium-high heat. 

Step 3
Once hot, add the filet mignon and sear until it develops a golden-brown crust on each side and is cooked to the desired doneness. For rare, cook for about 2 minutes on each side. For medium-rare, cook for about 4 minutes on each side. For medium, cook for about 5 minutes on each side. You can double-check the cooking by reading the internal temperature of the meat with a meat thermometer. (See below for cooking temps) 

Step 4
Remove the filets from the skillet and rest for at least 10 minutes. 

Step 5
While the filet mignon rests, make the shallot cream sauce. Add the butter to the same skillet used to sear the steak over medium heat.

Step 6
Add the finely chopped shallots and sauté until soft and translucent, about 5 minutes. Then add the minced garlic.

Step 7
Next, add the cracked black peppercorns and sauté for another minute.

Step 8
Deglaze the skillet with beef broth, scraping up any browned bits from the bottom of the skillet.

Step 9
Stir in the heavy cream and bring to a simmer. Cook until the sauce thickens slightly, about 5-7 minutes. 

Step 10
Lastly, add in the salt.

Serve the filet mignon with a spoonful of shallot cream sauce drizzled on top or below each filet. Top with herbs for a finishing touch if desired.