Add onion and bell pepper and cook until softened, about 3–4 minutes.
Add spinach and cook just until wilted. Transfer vegetables to a plate.
Crack eggs into a bowl, season with salt and black pepper, and whisk well.
Reduce heat to medium-low and pour eggs into the skillet.
When the eggs are mostly set but still soft on top, spread the cooked vegetables over one half of the omelette. Add cheese if using.
Carefully fold the omelette in half and cook for 1 more minute until fully set but tender.
Slide onto a plate and serve immediately.
