Crack 2 large eggs into a medium bowl and whisk until yolks and whites are well combined. Season the eggs with sea salt and freshly ground black pepper to taste.

Heat an 8-inch nonstick skillet over medium heat until warm. Add butter or extra-virgin olive oil to the pan and swirl to coat the bottom.

Pour the whisked eggs into the skillet and immediately reduce the heat to medium-low.

Cook without stirring until the edges just begin to set, about 10 seconds.

Working around the edges with a spatula, gently push the cooked egg toward the center so uncooked egg flows to the outside; tilt the pan as needed. Repeat until the uncooked egg thickens and the omelette forms an even layer.

When the omelette is mostly set but still slightly soft on top, add your desired fillings on one half.

Fold the other half of the omelette over the fillings and cook until the eggs are just set.

Remove the omelette from the heat, adjust seasoning with sea salt and freshly ground black pepper if desired, and serve.