Prepare the Basil Compound Butter: In a medium bowl, combine softened butter, chopped basil, lemon juice, and salt. Mix until well combined. Transfer the mixture onto a piece of plastic wrap and shape it into a log. Wrap tightly and refrigerate until firm, about 30 minutes.

Prepare the Filet Mignon: Preheat your oven to 400°F (200°C). Pat the filet mignon steaks dry with paper towels, then season both sides with salt and freshly ground black pepper. In a small bowl, mix together the sun-dried tomatoes, fresh oregano, breadcrumbs, and grated Parmesan cheese. Press the mixture firmly onto the top of each filet mignon to create a crust.

Sear the Steaks: Heat olive oil in an oven-safe skillet over medium-high heat. Once hot, add the filet mignon, crust side down, and sear for 3-4 minutes until golden brown. Carefully flip the steaks over and sear the other side for an additional 2 minutes.

Bake the Steaks: Transfer the skillet to the preheated oven and bake for 6-8 minutes for medium-rare, or until desired doneness is reached. Remove from the oven and let the steaks rest for 5 minutes.

Serve: Slice the compound butter into rounds and place on top of the warm filet mignon just before serving. Garnish with additional fresh basil if desired.