Heat oil in a large skillet over medium-high heat. Add onion, bell peppers, and mushrooms; sauté 5 minutes. Combine onion mixture and next 5 ingredients (through beef) in a bowl. Shape beef mixture into 8 (1/3-inch-thick) patties.
Heat a grill pan over high heat; coat with cooking spray. Cook patties 3 minutes; turn, top with cheese, and cook 2 minutes.
Arrange buns, cut sides up, on a baking sheet; broil 30 seconds. Assemble sandwiches.
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