Caramelize the onions: In a skillet, heat the butter and olive oil over medium heat. Add the diced onions and cook slowly, stirring often, until golden and caramelized (about 10 minutes).
Sauté the mushrooms: Add the chopped mushrooms to the same pan and cook until tender and browned. Season the mixture with salt and pepper to taste
Prepare the eggs: Beat the eggs with a pinch of salt and pepper. Pour into a seperate heated pan and let cook gently until just beginning to set.
Assemble the omelet: Spoon the mushroom and onion mixture onto one half of the omelet. Sprinkle cheese over the top.
Fold and finish: Gently fold the omelet over and cook for another minute until the cheese is melted and the eggs are cooked through (but still soft).
Serve: Slide the omelet onto a plate and serve with a mixed salad dressed in Uber Lemony Dressing for a complete, flexible meal.