Heat the oil in a large skillet over medium heat. Add the onion and cook until softened, about 5 minutes. Add in the mushrooms and continue to cook until soft and tender, another 5-10 minutes. Add in the red pepper flakes, then season with salt and pepper. Stir in the spinach and cook until the spinach has wilted.

Place the oven rack 4-5 inches from the heat and preheat the oven broiler.

Place the tortillas in a single layer on a baking sheet. Place the sheet in the oven and bake until the tortillas are golden, 1 to 2 minutes. Remove from the oven. Remove 4 of the tortillas. Divide the mushroom mixture between the 4 tortillas on the baking sheet. Sprinkle with the cheese, then place back in the oven until the cheese has melted, 1 to 2 minutes. Remove and sprinkle on the cilantro, then top with the reserved tortillas. Serve with the salsa.