Preheat the oven to 425°F. Spray a large baking sheet with nonstick spray.
Whisk together the eggs and water. Pour into a heated and greased skillet and scramble. Season the eggs with salt and pepper.
Stir in the green chiles and cheese.
Spoon the egg mixture evenly down one side of the tortillas. Roll up tightly. Place the seam side down on a baking sheet. Spray the tops with nonstick baking spray. Bake for 12-15 minutes. Serve hot with salsa.
The taquitos can also be frozen before you bake them. Lay them on a wax paper lined tray and freeze for 30 minutes. Place the frozen rolls in a freezer bag. Bake the frozen taquitos at 425°F for 20-22 minutes.