Step 1: Prepare and Season the Filet Mignon

1. Season the Filet: Pat the filet mignon dry with paper towels, which helps ensure a good sear. Season both sides generously with salt and freshly ground black pepper. Allow the steaks to sit at room temperature for about 15-20 minutes. This helps them cook evenly.
2. Preheat the Skillet: In a heavy-bottomed skillet, such as cast iron, heat the olive oil over medium-high heat. The oil should be hot and shimmering before you add the steak, ensuring a good sear.
3. Add the Filet to the Skillet: Place the seasoned filet mignon in the hot skillet and sear for about 3-4 minutes on each side. For even cooking, resist the urge to move the steak around, allowing it to form a beautiful, golden-brown crust.
4. Add Butter and Aromatics: During the last minute of searing on each side, add the butter and fresh thyme or rosemary (if using). Spoon the melted butter over the filet, basting it for extra flavor.
5. Check for Doneness: Use an instant-read thermometer to check the internal temperature. For medium-rare, aim for around 130°F, while medium is closer to 140°F. Remove the filet from the skillet when it’s 5-10 degrees below your desired doneness, as it will continue to cook as it rests.
6. Rest the Filet: Transfer the filet mignon to a plate and cover loosely with foil. Let it rest for 5-10 minutes, which allows the juices to redistribute and results in a tender, juicy steak.

Step 2: Prepare the Peppercorn Sauce

1. Deglaze the Skillet: After removing the steak, reduce the skillet to medium heat. Pour in the brandy or cognac to deglaze the pan, scraping up any browned bits from the bottom. If not using alcohol, substitute with beef broth for a similar depth of flavor.
2. Add Broth and Cream: Once the liquid has reduced by half, add the beef broth and let it simmer for 2-3 minutes until slightly thickened. Stir in the heavy cream, allowing it to blend with the beef flavors.
3. Incorporate Mustard and Peppercorns: Add the Dijon mustard and crushed peppercorns, stirring to combine. Adjust the heat to medium-low and let the sauce simmer gently for 4-5 minutes, or until it reaches your desired consistency. The sauce should be creamy and lightly coat the back of a spoon.
4. Finish with Butter: Stir in the butter to give the sauce a smooth, glossy finish. Taste and season with salt if needed, keeping in mind that the peppercorns add their own heat and flavor.

Step 3: Plate and Serve

1. Plate the Filet Mignon: Place each filet mignon on a plate. Pour the peppercorn sauce generously over the top or serve it on the side.
2. Garnish and Serve: Garnish with fresh herbs like parsley or thyme for an added touch of elegance. Serve immediately while the filet and sauce are warm and at their peak flavor.