Preheat the oven to 400°F (200°C). Season the beef tenderloin with salt and black pepper.
Heat olive oil in a skillet over medium-high heat. Sear the beef on all sides until browned, about 3 minutes per side.
Transfer the beef to a baking sheet and roast for 20-25 minutes or until the internal temperature reaches 130°F for medium-rare.
In the same skillet, melt butter and sauté shallots and garlic until fragrant.
Add the mushrooms and cook until softened, about 5 minutes.
Deglaze the pan with white wine, scraping up any browned bits.
Stir in the heavy cream, beef broth, Dijon mustard, and thyme. Simmer until thickened, about 5 minutes.
Remove the beef from the oven and let it rest for 10 minutes before slicing.
Stir Parmesan cheese into the sauce and serve over sliced beef tenderloin.