Step 1: Remove the filet mignon from the refrigerator and allow them to sit at room temperature for about 30 minutes. Generously season both sides with salt and freshly ground black pepper.
Step 2: In a large skillet, heat the olive oil over medium-high heat until shimmering. Add the filet mignon to the hot skillet and sear for about 4-5 minutes on each side for medium-rare, adjusting the time for your desired doneness. For medium, add an extra minute per side. Use a meat thermometer to check for doneness (130°F for medium-rare).
Step 3: In the last minute of cooking, add the butter to the pan. As it melts, spoon the butter over the steaks to baste them. Remove the steaks from the skillet and let them rest on a plate, loosely covered with foil.
Step 4: In the same skillet, reduce the heat to medium and add the whole peppercorns. Toast them for about 1 minute until fragrant, stirring frequently.
Step 5: Add the chopped shallot to the skillet and sauté for 2-3 minutes until softened and translucent.
Step 6: Pour in the beef broth, scraping up any browned bits from the bottom of the pan. Allow it to simmer for about 3-4 minutes until reduced by half.
Step 7: Stir in the heavy cream and Dijon mustard, bringing the sauce to a gentle simmer. Cook for an additional 2-3 minutes until the sauce thickens slightly. Season with salt to taste.
Step 8: Slice the filet mignon if desired and place it on plates. Drizzle the peppercorn sauce generously over the steaks and garnish with fresh parsley.