Heat a grill or large nonstick skillet over med-high heat.
Place meat in a bowl; add in shallots, sage, parsley, chopped garlic, Worcestershire, grill seasoning, and a healthy drizzle of olive oil; mix gently but thoroughly.
Score mixture into 4 quarters; for each portion into 1-inch thick patties.
Cook the patties for 5-6 minutes on each side.
Place the cheese on top of the patties in the last 2 minutes of cooking time and loosely tent the pan with foil to melt the cheese.
While the burgers cook, heat a skillet over med-high heat; add in 2 tablespoons olive oil and the butter; when the butter melts, add ¾ of the sliced onions and the sliced mushrooms; cook about 8-10 minutes, until the mushrooms are a deep brown, stirring often.
Season the mushrooms with salt and pepper after they brown.
Add in the Marsala; cook it down to glaze the mushrooms with its flavor; remove pan from heat.
Brown the split rolls under the broiler and rub lightly with the cracked garlic.
Drizzle the rolls lightly with olive oil and top with cheese covered burgers and a pile of Marsala mushrooms.