Begin by generously seasoning both sides of the filet mignon with salt and freshly cracked black pepper. Ensure the steak reaches room temperature, allowing for even cooking.

Heat the skillet over medium-high heat and add a small amount of oil. Carefully place the seasoned filet mignon in the skillet, searing for 3-4 minutes on each side.

Remove the filet mignon from the skillet and transfer it to a cutting board. Allow it to rest for at least 5 minutes.

In the same skillet, lower the heat to medium and add finely chopped shallots. Sauté until they turn translucent, approximately 2-3 minutes.

Pour in the red wine and add fresh thyme for aroma; bring the mixture to a gentle simmer, allowing it to reduce by half, about 5-7 minutes.

Stir in the beef broth, continuing to simmer for another 5 minutes, creating a rich sauce that complements your steak.

Stir in a couple of tablespoons of butter until melted, creating a glossy texture. Taste and adjust seasoning as needed.

Slice the filet mignon against the grain into thick medallions and arrange them on a serving platter. Drizzle the red wine sauce over the steak and garnish with fresh thyme.