Remove the filet mignon steaks from the refrigerator and let them sit at room temperature for 10 minutes.
Season both sides of the steaks evenly with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Add the filet mignon steaks to the skillet and sear for 4 minutes on each side for medium-rare, or until desired doneness is reached.
Remove the steaks from the skillet, cover loosely with foil, and let rest while preparing the sauce.
Reduce heat to medium and add butter to the same skillet.
Once the butter has melted, add the sliced mushrooms and sauté for 5 minutes until they release their moisture and start to brown.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the white wine and cook for 2 minutes, scraping up any browned bits from the skillet.
Add the beef broth and bring to a simmer. Cook for 3 minutes until the sauce reduces slightly.
Stir in the heavy cream and fresh thyme leaves. Simmer for another 2 minutes until the sauce thickens.
Return the filet mignon steaks to the skillet and spoon the mushroom sauce over them to warm through for 1-2 minutes.
Serve the filet mignon topped with the mushroom sauce immediately.