Spray a skillet with cooking spray and heat over medium. Whisk eggs with 1-2 tablespoons of water in a small bowl (the water helps to fluff the omelet). Chop mushrooms.
Pour half the eggs into hot skillet and sprinkle with half the ham and mushrooms. Cook until the eggs begin to set, then push the eggs towards the center of skillet and allow the uncooked eggs to move around. Cook for 1 minute longer and then flip.
Sprinkle half the cheese over the eggs and top with one tortilla. Flip over so that the tortilla is now on the bottom in the skillet; place another tortilla on top. Continue to cook for 30 seconds and then flip over again, cooking for another 30 seconds; this will allow the tortillas to brown. Remove from skillet and slice in half. Repeat with remaining ingredients.