In a non-stick skillet over medium heat, melt half of the butter. Add the sliced mushrooms and sauté for 3-4 minutes until browned and tender. Remove mushrooms from the pan and set aside.

Crack the eggs into a bowl. Season with a pinch of salt and white pepper. Whisk vigorously with a fork until the whites and yolks are completely combined and no streaks remain.

Wipe the skillet clean and return it to medium-low heat. Add the remaining butter and swirl to coat the pan. Do not let the butter brown.

Pour the eggs into the pan. Using a rubber spatula, continuously stir the eggs in a circular motion while shaking the pan back and forth to create small curds.

When the eggs are softly set but still creamy on top (resembling wet scrambled eggs), stop stirring. Smooth the surface slightly with the spatula.

Sprinkle the sautéed mushrooms and grated Gruyère in a line across the center of the eggs.

Tilt the pan slightly and use the spatula to gently roll the omelette down over the filling, creating a cylinder shape.

Invert the pan over a plate to turn the omelette out, seam side down. Brush with a little extra butter or truffle oil if desired, and garnish with fresh chives.