Heat half the butter or oil in a non-stick pan. Add bell peppers and onions and sauté for 2–3 minutes until softened. Add spinach and cook until wilted. Remove vegetables from the pan.
In a bowl, whisk the eggs with salt, pepper, and milk or cream if using.
Wipe the pan and add the remaining butter. Pour in the eggs and tilt the pan to spread evenly. Let the eggs cook undisturbed for 1–2 minutes.
Once mostly set, add the sautéed vegetables and shredded cheese to one half of the omelette. Fold the other half over the filling. Cook for another minute until the cheese melts.
Slide onto a plate and serve immediately.