01 - Remove the filet mignon steaks from the refrigerator approximately 30 minutes before cooking to allow them to reach room temperature. Pat the steaks thoroughly dry with paper towels, then generously season both sides with salt and freshly ground black pepper.
02 - Heat 1 tablespoon of olive oil in a heavy-bottomed skillet or cast-iron pan over medium-high heat. Once the oil is shimmering and hot, carefully place the seasoned steaks into the pan. Sear for 2 to 3 minutes per side until a rich, deep golden-brown crust has formed.
03 - Reduce the heat to medium. Add 1 tablespoon of unsalted butter, the fresh thyme sprigs (if using), and the crushed garlic to the pan. Continuously spoon the melted butter mixture over the steaks for 1 to 2 minutes. Cook until the desired internal doneness is reached (for instance, 125°F for rare or 135°F for medium-rare).
04 - Carefully transfer the cooked steaks to a clean plate. Tent them loosely with aluminum foil to retain warmth and allow them to rest while you prepare the shrimp. This step is crucial for juicy steaks.
05 - If necessary, wipe out any residual bits from the skillet. Return the skillet to medium heat and add 1 tablespoon of unsalted butter and 1 tablespoon of olive oil. Once the butter is melted, add the minced garlic and cook for about 30 seconds until it becomes fragrant.
06 - Add the peeled and deveined shrimp to the skillet in a single layer. Cook for 1 to 2 minutes per side, or until the shrimp turn opaque and develop a vibrant pink color.
07 - Stir in the fresh lemon juice, chopped fresh parsley, and chili flakes (if using). Season the shrimp with salt and pepper to taste, ensuring all flavors are well incorporated.
08 - Arrange the rested steaks on individual serving plates. Top each steak generously with the sautéed shrimp. Garnish with additional chopped fresh parsley and lemon wedges. Serve immediately for the best experience.