In a bowl, combine the softened butter, minced black garlic, chopped shallot, lemon zest, and lemon juice. Mix until well blended. Place the compound butter onto a piece of parchment paper, shape into a log, and refrigerate until firm.

Preheat your oven to 400°F (200°C).

In a skillet, heat 1 tablespoon of olive oil over medium heat. Add the sliced leeks and thyme, cooking until the leeks are softened and starting to caramelize, about 8-10 minutes. Season with salt and pepper. Set aside.

Season the filet mignon steaks generously with salt and pepper on both sides. In the same skillet, add the remaining tablespoon of olive oil and heat over high heat. Once hot, sear the steaks for 3-4 minutes on each side until a golden crust forms.

Transfer the seared steaks to a baking dish. Top each steak with the sautéed leeks. Roast in the preheated oven for about 10-12 minutes for medium-rare, or until your desired doneness is reached.

Remove the steaks from the oven and let them rest for 5 minutes. Slice the chilled compound butter into rounds and place on top of each steak just before serving. Serve hot, garnished with additional thyme if desired.