01 - Remove the filet mignon steaks from the refrigerator 30 minutes prior to cooking to allow them to reach room temperature. Thoroughly pat them dry with paper towels and season generously on both sides with kosher 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, carefully place the seasoned steaks into the hot 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, fresh thyme sprigs (if using), and crushed garlic cloves to the pan. Continuously spoon the melted butter mixture over the steaks for 1 to 2 minutes, cooking until your desired doneness is achieved (target 125°F for rare, 135°F for medium-rare).
04 - Transfer the cooked steaks to a clean plate. Loosely tent them with aluminum foil and allow them to rest while you prepare the shrimp. This step is crucial for juicy steaks.
05 - If necessary, quickly wipe out any excess residue from the skillet. Return the skillet to medium heat and add 1 tablespoon of unsalted butter and 1 tablespoon of olive oil. Add the minced garlic and cook for approximately 30 seconds until its aroma is pronounced.
06 - Arrange the peeled and deveined shrimp in a single layer in the skillet. Cook for 1 to 2 minutes per side, just until they turn opaque and pink, indicating they are cooked through.
07 - Stir in the fresh lemon juice, chopped fresh parsley, and chili flakes (if desired). Season the shrimp with additional salt and pepper to taste.
08 - Carefully place the rested steaks onto serving plates. Top each steak generously with the sautéed garlic butter shrimp. Garnish with additional fresh parsley and lemon wedges. Serve this elegant dish immediately for the best experience.