Prepare the Compound Butter: Preheat your oven to 400°F (200°C). Place the shallot on a small piece of aluminum foil, drizzle with a little olive oil, and season with salt and pepper. Wrap the shallot in the foil and roast in the oven for about 20-25 minutes, or until tender.

In a mixing bowl, combine the softened butter, roasted shallot (after it has cooled slightly and minced), and chopped chives. Mix well until all ingredients are evenly incorporated. Season with salt and pepper to taste.

Transfer the compound butter onto a piece of parchment paper, shape it into a log, and roll it tightly. Chill in the refrigerator until firm.

Prepare the Filet Mignon: In a dry skillet over medium heat, toast the black peppercorns and fennel seeds for about 2-3 minutes, or until fragrant. Remove from heat and let cool slightly.

Once cooled, transfer the spices to a spice grinder or mortar and pestle and grind them coarsely.

Pat the filet mignon steaks dry with paper towels. Rub each steak with olive oil and season generously with salt. Press the spice mixture firmly onto both sides of the steaks.

Cook the Filet Mignon: Heat a large skillet over medium-high heat. Once hot, add the seasoned filet mignon. Cook for about 4-5 minutes on each side for medium-rare, or until desired doneness is reached. Use a meat thermometer if necessary (130°F/54°C for medium-rare).

Remove the steaks from the skillet and let them rest for 5-10 minutes.

Serve: Slice the chilled compound butter into rounds. Place a slice on top of each filet mignon steak just before serving, allowing it to melt over the warm meat. Enjoy your delicious Black Pepper and Fennel Seed-Crusted Filet Mignon with Roasted Shallot and Chive Compound Butter!