In a large skillet, heat oil over medium heat. Add onion and cook, stirring until softened, about 5 minutes. Add the mushrooms and cook until tender, about 5 minutes. Add the red pepper and cook about 30 seconds. Season with salt and pepper. Stir in the spinach and cook, stirring until it has wilted,about 2 minutes. Remove pan from heat.
Position oven rack 4-5 inches from the heat and preheat the broiler to medium.
Place the tortillas in a single layer on a baking sheet and broil until golden, 1-2 minutes. Remove the pan from oven and top half the tortillas with spinach mixture. Remove other tortillas from the baking sheet. Sprinkle the tortillas on the baking sheet with cheddar and cilantro and place back under the broiler until cheese has melted, 1-2 minutes. Top the mushroom tortillas with the plain tortillas and serve with salsa.