Meanwhile, spray 10-inch skillet with cooking spray; heat over medium heat. Cook mushrooms and onion in skillet about 4 minutes, stirring frequently, until onion is crisp-tender. Stir in beans; heat through. Stir in spinach; remove from heat.
Divide bean mixture among tortillas.
Sprinkle with cheese. Fold one end of each tortilla up about 1 inch over filling; fold right and left sides over folded end, overlapping. Fold remaining end down.