Pat the steaks dry with paper towels and season both sides generously with salt and freshly ground black pepper.

Heat 1 tablespoon of butter and the olive oil in a large skillet over medium-high heat until the butter is melted and foaming.

Add the steaks to the hot skillet and sear for 3 to 4 minutes per side for medium-rare, or until a beautiful golden-brown crust forms.

Transfer the steaks to a warm plate, tent loosely with aluminum foil, and let them rest while you prepare the sauce.

Lower the heat to medium, add the remaining 1 tablespoon of butter to the same skillet, then stir in the minced shallots and sliced mushrooms.

Cook the shallots and mushrooms for 3 to 4 minutes, stirring occasionally, until the mushrooms are tender and lightly browned.

Stir in the minced garlic and cook for about 30 seconds until fragrant, being careful not to let the garlic burn.

Pour in the cognac to deglaze the pan, scraping up any browned bits from the bottom, and let it simmer for 1 minute until mostly evaporated.

Whisk in the Worcestershire sauce, Dijon mustard, and beef broth, bringing the mixture to a simmer for 2 minutes to reduce slightly.

Pour in the heavy cream and simmer for 2 to 3 minutes, stirring constantly, until the sauce thickens enough to coat the back of a spoon.

Return the rested steaks and any accumulated juices to the skillet, spooning the rich cream sauce over the meat to warm through for 1 minute.

Garnish with freshly chopped chives and serve immediately alongside roasted potatoes or crusty bread to soak up the luxurious sauce.