01 - Remove the filet mignon from refrigeration approximately 30 minutes prior to cooking to allow it to reach room temperature. Thoroughly pat dry the steaks with paper towels to ensure optimal searing.
02 - Preheat your oven to 400°F.
03 - Liberally season both surfaces of the filet mignon steaks with kosher salt and freshly ground black pepper.
04 - Place a heavy, oven-safe skillet (such as cast iron) over medium-high heat and add the olive oil.
05 - Once the oil is shimmering, carefully place the seasoned steaks in the hot skillet. Sear for 2 to 3 minutes per side, aiming for a rich golden-brown crust.
06 - Introduce the unsalted butter to the skillet. As it melts, continuously spoon the rendered butter over the searing steaks to enhance flavor.
07 - Carefully transfer the skillet containing the steaks to the preheated oven. Roast for 5 to 7 minutes for a medium-rare doneness (internal temperature approximately 130°F), or adjust the cooking time to achieve your preferred level of doneness.
08 - Upon reaching desired doneness, remove the steaks from the oven and transfer them to a clean plate. Tent loosely with aluminum foil and allow them to rest for 5 minutes; this is crucial for retaining juices and tenderness.
09 - While the steaks rest, combine the balsamic vinegar, honey, and finely chopped fresh rosemary in a small saucepan. Bring the mixture to a gentle boil over medium heat, then reduce the heat to a simmer. Continue to cook for 6 to 8 minutes, stirring periodically, until the mixture has reduced by half and achieved a syrupy consistency.
10 - Arrange the rested filet mignon steaks on serving plates. Drizzle generously with the warm, syrupy balsamic reduction. Optionally, garnish with fresh rosemary sprigs or microgreens for an elegant presentation.