Preheat the oven to 400°F (200°C).
Season the beef tenderloin with salt and pepper.
Heat a skillet over medium-high heat and sear the beef on all sides until browned, about 2-3 minutes per side.
While the beef sears, roughly chop the white button mushrooms to form a thick layer that can wrap around the beef.
Lightly sauté the mushrooms in the skillet with a dash of salt and a sprig of thyme until they soften slightly, about 2-3 minutes.
Place the seared beef on a clean surface and carefully wrap it with the sautéed mushrooms, ensuring most of the surface is covered.
Toss the roasted root vegetables with olive oil, salt, pepper, and the remaining thyme.
Arrange the mushroom-wrapped beef and the prepared root vegetables on a baking tray.
Roast in the preheated oven until the beef reaches your preferred doneness (about 8-10 minutes for medium-rare), and the vegetables are tender.
Remove from the oven, let the beef rest for a few minutes, then slice and serve alongside the roasted vegetables.