Season the filet mignon steaks generously with salt and freshly ground black pepper on both sides.

In a small skillet over medium heat, add 1 tablespoon of olive oil. Add the minced garlic and thyme leaves. Cook, stirring frequently, until the garlic is caramelized and golden brown, about 5-7 minutes. Remove from heat and let it cool slightly.

Preheat your oven to 400°F (200°C). Spread the caramelized garlic mixture evenly over the top of each steak, pressing it gently to adhere.

In a large, oven-safe skillet, heat the remaining 2 tablespoons of olive oil over high heat. Once the oil is hot, add the filet mignon steaks and sear for 2-3 minutes on each side, until a nice crust forms.

Transfer the skillet to the preheated oven and roast for 6-8 minutes for medium-rare, or until your desired doneness is reached. Use a meat thermometer for accuracy (130°F for medium-rare).

Remove the skillet from the oven and transfer the steaks to a plate to rest. On the stovetop, carefully add the cognac to the skillet, using a wooden spoon to scrape up any browned bits from the bottom. Add the whole black peppercorns and cook for 1-2 minutes. Pour in the heavy cream and bring to a simmer. Cook until the sauce thickens slightly, about 3-5 minutes. Season with salt to taste.

In a small bowl, mix the softened butter with the chopped tarragon until well combined. Season with a pinch of salt.

Slice the filet mignon and plate it with a drizzle of the cognac peppercorn sauce. Add a dollop of tarragon butter on top and garnish with fresh thyme sprigs if desired. Enjoy!