Crack the eggs into a bowl, add milk or water if using, and whisk until combined and slightly frothy.
Season with a pinch of salt and black pepper.
Heat the butter or oil in a nonstick skillet over medium heat until melted and hot.
Add the spinach and cook briefly until it just begins to wilt.
Pour the egg mixture evenly over the spinach in the pan.
Let the eggs cook without stirring until the edges begin to set.
Sprinkle the shredded cheese over the omelette.
When the top is mostly set but still slightly soft, use a spatula to fold the omelette in half.
Cook another minute until the cheese is melted and the eggs are cooked through.
Slide the omelette onto a plate and serve warm.