Chop enough of the sliced onion to measure 1/4 cup. Combine chopped onion, beef, 1/8 teaspoon salt, and 1/8 teaspoon pepper in a medium bowl. Divide beef mixture into 4 equal portions with moist hands, shaping each into a 4-inch oval patty. Press thumb in center of each patty, leaving a nickel-sized indentation.
Heat a large nonstick skillet over medium-high heat. Add 1 teaspoon oil to pan, swirling to coat. Add patties; cook 4 minutes on each side or until done.
Heat 2 teaspoons oil in a medium skillet over medium-high heat. Add mushrooms, remaining onion, 1/8 teaspoon salt, and 1/8 teaspoon pepper; sauté 3 minutes. Sprinkle flour over mushroom mixture; cook 1 minute, stirring constantly. Stir in beer; cook 30 seconds or until thick. Remove from heat; keep warm.
When patties are done, remove from large pan. Wipe pan clean; heat over medium-high heat. Coat 1 side of each bread slice with cooking spray. Place 4 bread slices, coated sides down, in pan. Top each with 1 patty, 1 cheese slice, and one-fourth of mushroom mixture. Top with remaining bread slices; coat with cooking spray. Cook 2 minutes on each side or until browned.
This updated version of Mushroom and Provolone Patty Melts is based on a recipe that originally ran in Cooking Light, October 2010. The recipe was retested and updated for Cooking Light Crave!, Oxmoor House, 2013.