Heat 1 tablespoon EVOO in a medium size skillet over medium-high heat. Sauté the mushrooms, onion and peppers until tender, 7-8 minutes, then season with salt and pepper. Deglaze the pan with stock.
Combine the sausage and sirloin with the grill seasoning, garlic and parsley. Mix and form four patties, thinner at the center and thicker at the edges for even cooking and to keep the burgers from bulging. Heat a cast iron or nonstick skillet with the remaining 1 tablespoon EVOO over medium-high heat. Cook the patties for 12 minutes, turning once, and top with the mushrooms, onion and peppers and two slices of cheese. Turn the heat off and cover the pan with foil to melt cheese, 2 minutes. Pile on buns and serve.