Preheat your grill or grill pan over medium-high heat.

Slice the eggplants into 1-inch thick rounds. Brush both sides with 2 tablespoons of olive oil and season with salt. Grill the eggplant for about 4-5 minutes per side, or until charred and tender. Remove from the grill and set aside.

In a small bowl, combine the cracked black peppercorns and a pinch of salt. Press this mixture into both sides of each filet mignon steak to create a crust.

In a large skillet, heat the remaining 2 tablespoons of olive oil over medium-high heat. Add the filet mignon steaks and cook for about 4-5 minutes on each side for medium-rare, or until desired doneness. Use a meat thermometer to check for an internal temperature of 130°F for medium-rare. Remove from the skillet and let the steaks rest for 5 minutes.

While the steaks are resting, prepare the whipped sun-dried tomato and basil butter. In a mixing bowl, combine the softened butter, sun-dried tomatoes, chopped basil, minced garlic, and balsamic vinegar. Mix well until all ingredients are combined and the mixture is creamy.

To serve, place a charred eggplant round on each plate. Top with a filet mignon steak and a generous dollop of the whipped sun-dried tomato and basil butter. Garnish with fresh basil leaves.