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Preheat a grill to medium heat.
For the mushroom sauce: Place a saucepan over medium-high heat and melt the butter. Add the mushrooms, salt, pepper and shallots and saute, stirring frequently until beginning to brown, 4 to 5 minutes. Pour in the wine to deglaze and cook until most of the liquid has evaporated, 4 minutes. Add the demi-glace, stock, cream and thyme leaves, and simmer until thickened just enough to coat the back of a spoon.
Meanwhile, remove the meat from the marinade. Coat with olive oil and sprinkle with salt and pepper. Grill until medium rare, 2 to 3 minutes. Let rest before slicing and serving with the mushroom sauce.