Prepare the Compound Butter: In a small skillet over medium heat, melt 1 tablespoon of the butter. Add the chopped shallot and sauté until translucent, about 3-4 minutes. Add the balsamic vinegar and cook until it reduces slightly, about 2-3 minutes. Remove from heat and let it cool slightly. In a bowl, combine the remaining 3 tablespoons of softened butter, sautéed shallot mixture, and freshly chopped parsley. Mix well until all ingredients are combined. Transfer the mixture onto a piece of parchment paper, roll it into a log shape, and refrigerate until firm.

Prepare the Steaks: Preheat your oven to 400°F (200°C). Season the filet mignon steaks generously with salt and freshly ground black pepper on both sides. In a large oven-safe skillet, heat the olive oil over medium-high heat. Once hot, add the steaks and sear for 3-4 minutes on each side until a golden crust forms.

Add Garlic and Rosemary: During the last minute of searing, add the minced garlic and chopped rosemary to the skillet, spooning the oil over the steaks to infuse flavor.

Roast in the Oven: Transfer the skillet to the preheated oven and roast for an additional 5-7 minutes for medium-rare, or until the desired doneness is reached. Use a meat thermometer for accuracy (130°F for medium-rare, 140°F for medium).

Rest and Serve: Once cooked to your liking, remove the skillet from the oven and let the steaks rest for 5 minutes. Slice the chilled compound butter into rounds and place a piece on top of each steak just before serving. Let it melt over the warm filet mignon. Garnish with additional fresh parsley if desired, and serve with your choice of sides.