Crack the eggs into a bowl. Add the water, salt and pepper and whisk until fully blended.
Melt the butter in an 8-inch nonstick skillet over medium heat, swirling to coat the pan.
Pour in the eggs. As the edges set, use a spatula to gently pull them toward the center, tilting the pan so the uncooked egg runs to the edges.
Cook for 1–2 minutes, until the eggs are mostly set but still a little moist on top.
Sprinkle the cheese over one half. Fold the other half over the cheese and cook for 30 seconds more, until melted.
Slide the omelet onto a plate and serve right away.
