Heat 1 teaspoon olive oil in a skillet over medium heat. Add 1 clove minced garlic and sauté about 30 seconds to 1 minute, until fragrant but not browned.
Add 8 ounces sliced mushrooms and sauté about 10 minutes, stirring occasionally, until the mushrooms are softened and most liquid has evaporated. Stir in 1 tablespoon minced parsley, then remove the pan from the heat and transfer the mushrooms to a plate; set aside.
In a bowl, whisk 3 large egg yolks until slightly thickened and uniform.
In a separate, clean bowl, beat 3 large egg whites until soft peaks form (white, glossy, and able to hold a gentle peak). You may use a whisk, electric mixer, or blender.
Gently fold the beaten egg whites into the yolks in two additions, using a spatula and a folding motion to preserve the air in the whites.
Fold 1/4 cup shredded fat-free cheddar into the combined egg mixture until just incorporated.
Spray a clean large skillet with nonstick spray and heat over low to medium-low. Pour in the egg mixture, cover with a lid, and cook until the bottom is set and the top is mostly set (about 3–5 minutes, depending on heat).
Carefully loosen the edges of the omelette with a spatula. Spoon the reserved mushrooms onto one half of the omelette, then fold the other half over the mushrooms.
Cover and cook 30 seconds to 1 minute more to warm the filling and melt the cheese, then transfer the omelette to a plate and serve hot.