Preheat your oven to 400°F (200°C).

In a small bowl, combine the crushed Szechuan peppercorns, chopped thyme, salt, and pepper. Mix well to create the seasoning blend.

Pat the filet mignon steaks dry with paper towels. Rub the olive oil over the steaks, ensuring they are evenly coated.

Generously coat each steak with the Szechuan peppercorn and thyme seasoning mixture, pressing it into the meat to adhere.

Heat a large oven-safe skillet over medium-high heat. Once hot, add the seasoned filet mignon steaks to the skillet. Sear for about 3-4 minutes on each side, until a golden-brown crust forms.

Transfer the skillet to the preheated oven and roast the steaks for 6-8 minutes for medium-rare, or adjust the cooking time based on your desired doneness.

While the steaks are roasting, prepare the brown butter shallot jus. In a small saucepan, melt the butter over medium heat. Add the chopped shallots and sauté until they become translucent and fragrant, about 3-4 minutes.

Pour in the beef broth and balsamic vinegar, stirring to combine. Bring the mixture to a simmer and let it reduce for about 5 minutes, until slightly thickened. Season with salt and pepper to taste.

Once the filet mignon has reached your desired doneness, remove it from the oven and let it rest for 5 minutes.

Serve the filet mignon drizzled with the brown butter shallot jus and garnish with fresh thyme sprigs.