In a large mixing bowl, combine the ground meats with the garlic, spices and chopped parsley. Score the meat into 4 equal portions then form patties thicker at edges and thinner at the center for even cooking.
Preheat a large, nonstick skillet with 1 tablespoon EVOO. Add the patties to the hot skillet and cook about 8 minutes total for medium rare, 10 minutes for medium, and 12 minutes for well-done, turning once.
Meanwhile, heat another large skillet over high heat with the remaining EVOO. Let the oil get hot, then add the mushrooms and sauté until golden brown. Toss in thyme and douse the mushrooms with the Marsala. Cook until reduced.
While the burgers and mushroom are cooking, spilt the rolls and toast them under the broiler.