Crack the eggs into a mixing bowl and whisk until well combined. Season with salt and pepper.

Melt butter in a non-stick skillet over medium heat, coating the surface well.

Pour the beaten eggs into the skillet, tilting the pan to spread the eggs evenly.

Allow the eggs to cook without stirring until the edges start to set, about 2-3 minutes. Gently lift the edges to let uncooked eggs flow underneath.

Once the eggs begin to firm up but are still slightly wet on top, sprinkle cheese and any optional vegetables onto one half.

Carefully fold the omelet in half and cook an additional 1-2 minutes until cheese is melted.

Slide onto a plate, garnish if desired, and serve warm.