Make the Basic Brown Sauce recipe (half) and keep it warm.
Let the steaks rest on the counter for 30 minutes.
Preheat the oven to 450ºF/230ºC
Gently pat the steaks dry and season generously with ground sea salt. Spread crushed peppercorns on all sides including the edges pressing down to adhere; set aside.
Heat up a cast iron pan on medium- high. When hot, add oil. Place meat and cook, undisturbed, for 2 to 2 ½ minutes (Maillard reaction).
Flip and cook the other side for 2 ½ minutes (medium-rare).
Add butter and garlic cloves. Tilt the pan to baste the meat, spooning on the butter a few times.
Transfer to the preheated oven and cook until desired doneness (refer to Filet Mignon • How to Cook Perfectly)
Remove the cast iron pan from the heat, pour in Cognac and ignite it.
When the flames go out, transfer the steaks onto a plate, cover loosely with foil and let them rest for 10 minutes.
In the same cast iron pan over medium-high heat with the two garlic cloves left in, add mushrooms and sauté until golden, about 2 to 3 minutes.
Season them with salt and pepper, stir well before transferring to a bowl and set aside. Discard the two garlic cloves.
Reduce the heat to medium-low to allow the cast iron pan to cool off a bit.
Add warm basic brown sauce and heavy cream. Stir and simmer for 2 minutes; taste and adjust seasonings if needed.
Before serving, add any accumulated juices to the sauce, stir well and spoon the sauce over the steaks and top with the sautéed mushrooms up. Serve with mashed potatoes and broccolini.