Preheat the oven to 350°F.

Season the beef tenderloin liberally with salt and black pepper on all sides. Drizzle with olive oil. Transfer the tenderloin to a baking dish and allow it to stand at room temperature for 15 minutes.

Roast the tenderloin on middle rack of oven until it reaches 130°F, 35-45 minutes. In the last 10 minutes of the roasting time, prepare the mushroom red wine sauce.

Check to see that tenderloin is done. Remove from oven or add time as needed. Tent with aluminum foil and allow to rest for 10 minutes.

Heat the butter in a large skillet over medium-high heat. Add the mushrooms and shallots, and season with salt and pepper. Saute until the mushrooms are shrunken and browned, and the shallots are translucent, 5-6 minutes. Add the garlic and continue cooking until fragrant, about 30 seconds.

Pour the red wine into the skillet to deglaze the pan, scraping up the browned bits on the bottom with a spatula. Add the beef broth and thyme sprigs. Allow the mixture to simmer until the liquid is reduced by half, 5-7 minutes. Stir in the heavy cream and continue simmering until heated through, 1-2 minutes.

Slice the tenderloin into 2- to 3-inch thick slices and arrange on a serving platter. Remove the thyme sprigs from the skillet and discard. Spoon the mushroom red wine sauce over the tenderloin slices, and serve immediately.