Crack the eggs into a bowl, add milk, salt, and pepper. Whisk until well combined.
In a non-stick pan, heat the butter or oil over medium heat. Add onions and mushrooms and sauté until soft and lightly golden.
Season the mushroom mixture with red pepper flakes and Italian seasoning. Remove and set aside.
In the same pan, pour in the egg mixture and swirl to coat the surface evenly. Let it cook for 1-2 minutes until the bottom is set.
Add the sautéed mushrooms and shredded cheese to one half of the omelet.
Fold the other half over the filling and cook for another minute or until the cheese is melted.
Slide onto a plate and serve hot.