Preheat oven to 240°C / 450°F (all oven types).
Tuck the thin tail end of the tenderloin under itself and tie with kitchen string at intervals to form a consistent shape for even cooking. Pat dry and rub all over with oil, salt, and pepper.
Place beef on a rack set over a roasting pan. Roast for 25 minutes for rare, 30 minutes for medium-rare, 35 minutes for medium (see note for beef tenderloin temperatures).
Remove beef from oven and transfer to a tray. Cover loosely with foil and rest for 20 minutes.
While beef is resting, make the sauce: melt butter in a skillet over high heat. Add mushrooms and cook until golden brown, around 5 minutes.
Add garlic and cook for 1 minute. Add wine/broth and stir, scraping up any brown bits from the bottom of the skillet.
Add beef broth, cream, mustard, and thyme. Bring to a simmer and cook for 5 minutes until it thickens slightly. Adjust seasoning to taste with salt and pepper.
Slice beef into thick slices and serve with mushroom sauce, garnished with parsley/chives.
Prep Time: 15 min | Total Time: 1 hr 15 min | Servings: 6