Preheat your oven to 400°F (200°C).

In a skillet over medium-high heat, add olive oil. Once hot, add the sliced leeks. Season with salt and pepper. Sauté the leeks until they are charred and softened, about 5-7 minutes. Remove from heat and let cool.

In a mixing bowl, combine the charred leeks, chopped sage, and breadcrumbs. Mix well until all ingredients are evenly distributed.

Season the filet mignon steaks with salt and pepper on both sides. Heat a skillet over high heat and add a tablespoon of olive oil. Once the oil is hot, sear the steaks for 2-3 minutes on each side until a golden-brown crust forms.

Remove the skillet from heat. Carefully press the leek-sage mixture onto the top of each filet mignon to form a crust.

Transfer the steaks to a baking dish and place them in the preheated oven. Cook for about 5-8 minutes for medium-rare, or until they reach your desired level of doneness.

While the steaks are baking, prepare the tarragon chive butter. In a small bowl, combine the softened butter, chopped tarragon, chopped chives, minced garlic, and lemon zest. Mix until well combined.

Once the steaks are done, remove them from the oven. Let them rest for a few minutes before serving.

Serve the filet mignon topped with a dollop of tarragon chive butter and enjoy!