2 tablespoons unsalted butter, divided
1/4 cup diced onion
1/2 cup sliced mushrooms
Kosher salt
Freshly ground black pepper
3 large eggs, whisked together with salt and pepper
1/4 cup shredded Gruyere (or other Swiss) cheese
Melt 1 tablespoon of the butter in a medium skillet pan over medium-high heat.
Add the onions and cook, stirring frequently, until softened, about 5 minutes.
Stir in the mushrooms and continue to cook, stirring often, until the mushrooms are softened, about 5 minutes more. Season to taste with salt and pepper.
Melt the remaining tablespoon of butter in an omelet pan over medium heat. Once the pan is hot, add the eggs.
As the egg begins to set, push it toward the center of the pan with a spatula and tip the pan to allow the uncooked egg to run underneath and around the cooked parts.
Once the eggs are mostly set, add the mushroom and onion mixture in a line down the center. Top with the cheese.
Fold the sides of the omelet up over the filling using a spatula.
Gently slide the omelet onto a plate and serve immediately.