Preheat oven to 350°F. Spray a nonstick muffin pan with olive oil spray.
Heat the oil in a large non-stick skillet over medium heat.
Sauté shallots and mushrooms with salt for 5 minutes, until soft, add garlic and saute another 3 minutes. Add spinach and cook 2 minutes more. Set aside.
Meanwhile, in a large bowl, whisk the egg whites with salt, pepper + nutmeg.
Spoon mushroom-spinach mixture into the prepared muffin tin. Distribute egg whites evenly to cover the veggies. Top each muffin with shredded Swiss.
Bake for 16 to 18 minutes, until set.