Step 1: Bring steaks to room temperature. Pat dry your filet mignon steaks thoroughly with paper towels. Season generously on all sides with kosher salt and freshly ground black pepper. Let them rest at room temperature for at least 30 minutes.
Step 2: Sear the steaks. Heat olive oil in a heavy-bottomed skillet (like cast iron) over high heat until shimmering and almost smoking. Carefully place the steaks in the hot pan. Sear for 3-5 minutes per side for medium-rare, or until a deep, golden-brown crust forms.
Step 3: Add butter and baste. Reduce heat to medium. Add butter to the pan. Tilt the pan and spoon the melted butter over the steaks for 1-2 minutes to infuse flavor. Use a meat thermometer to check for desired doneness (e.g., 130-135°F for medium-rare).
Step 4: Rest the steaks. Remove the steaks from the pan and place them on a cutting board or plate. Tent loosely with foil and let them rest for 5-10 minutes. This is crucial for juicy steaks.
Step 5: Prepare peppercorn sauce. While steaks rest, return the same skillet to medium heat. Add the crushed black peppercorns and minced shallot. Sauté for 1-2 minutes until fragrant and shallots are softened.
Step 6: Deglaze and simmer. If using, carefully add brandy or cognac to deglaze the pan, scraping up any browned bits from the bottom. Cook until almost evaporated. Stir in the beef broth and bring to a simmer, reducing by about half (2-3 minutes).
Step 7: Finish the sauce. Pour in the heavy cream and whisk in the Dijon mustard. Continue to simmer gently for 3-5 minutes, or until the sauce thickens to your desired consistency. Taste and adjust seasoning as needed.
Step 8: Serve. Slice the rested filet mignon against the grain, if desired, or serve whole. Drizzle generously with the creamy peppercorn sauce and garnish with fresh chopped parsley.