Heat you galley stove to over 400º or as hot as you can get it.
Mince the garlic and rosemary.
Rub the filet with salt and fresh ground black pepper. Place a large skillet on a medium to hot burner and let heat up until almost smoking. Sear the filet on all sides.
Let the filet cool a bit and rub with the garlic and rosemary. Place in a roasting pan and place in your pre-heated oven for about 30 minutes or until an instant-read thermometer reads 120º.
Chop the mushrooms, minced the shallots and press the garlic. In a large sauce pan, heat up the olive oil and butter. Mushrooms soak up a lot of oil, that’s why the generous amount of oil and butter. They also shouldn’t be crowded. The amount of moisture they put out will make them “steam” rather than fry. Sauté the 3 ingredients in the oil-butter mixture, stirring, until mushrooms turn dark brown. This will take over 10 minutes. The long heating time allows the rich flavor of the mushrooms to come through.
Once the filet is out of the oven, let rest for 10 minutes before slicing.