In a bowl, combine the softened unsalted butter, mashed black garlic, and lemon juice. Mix until well combined and smooth. Place the mixture on a piece of plastic wrap, roll it into a log shape, and refrigerate until firm.

Pat the filet mignon steaks dry with paper towels. Season both sides generously with salt and pepper.

In a small bowl, mix the minced garlic and chopped rosemary together. Press the garlic and rosemary mixture onto the top of each steak, ensuring it sticks well.

Heat olive oil in a large skillet over medium-high heat. Once hot, add the filet mignon steaks crust side down. Sear for about 4-5 minutes until the crust is golden brown.

Carefully flip the steaks and cook for an additional 3-4 minutes for medium-rare, or until desired doneness is reached. Use a meat thermometer to check the internal temperature (130°F for medium-rare).

Remove the steaks from the skillet and transfer them to a cutting board. Let the steaks rest for 5-10 minutes to allow the juices to redistribute.

Slice the compound butter into rounds and place a slice on top of each filet mignon. Garnish with fresh rosemary sprigs and serve immediately.