Mix meat, parmesan cheese, 1 1/4 cups water and onions until just blended. Shape into 6 (1/2 inch thick) oval patties. Place on a rimmed baking sheet or baking stone.
Bake 25 minutes or until done (160F). Meanwhile, cook mushrooms in a large nonstick skillet on medium-high heat for 5 minutes or until tender, stirring occasionally. Stir in barbecue sauce and remaining water; simmer on low heat 1 to 2 minutes or until heated through.