Prepare the Black Garlic Compound Butter: In a mixing bowl, combine the softened butter, mashed black garlic, chopped fresh thyme, and lemon juice. Mix until all ingredients are well incorporated. Transfer the mixture onto a piece of plastic wrap and shape it into a log. Wrap tightly and refrigerate until firm, about 30 minutes.

Prepare the Steaks: Remove the filet mignon from the refrigerator and let it come to room temperature, about 30 minutes. Preheat your oven to 400°F (200°C). Pat the steaks dry with paper towels and season both sides generously with salt, cracked black pepper, and fresh thyme leaves.

Sear the Steaks: In a large, oven-safe skillet, heat the olive oil over medium-high heat until shimmering. Add the filet mignon to the skillet and sear for about 3-4 minutes on each side, until a nice crust forms.

Bake the Steaks: Transfer the skillet to the preheated oven and cook for an additional 5-7 minutes for medium-rare, or until desired doneness is reached. Use a meat thermometer to check for doneness (130°F for medium-rare).

Serve: Remove the skillet from the oven and let the steaks rest for 5 minutes. Slice the chilled black garlic compound butter into rounds and place a slice on top of each steak just before serving.