Sprinkle filet with salt, pepper and drizzle oil. Place over a rack and a baking pan and cook over low heat, 225°F for 1-1⁄2 hours. Remove from the oven, cover with foil, and set aside for 10 minutes.
Place all mushrooms, basil leaves, thyme sprigs, garlic, salt and pepper into a baking pan. Drizzle with olive oil and broil for 10 minutes. Mix and set aside.
In a large pot, prepare the sauce. Off the heat, add the cooked mushrooms to the sauce and the juices from
beef pan if any and cook for 1 minute more. If too thick add milk.