Finely chop all vegetables so they cook quickly and evenly.
Crack the eggs into a bowl, add salt and black pepper, and whisk until well combined.
Heat olive oil or butter in a non-stick pan over medium heat.
Add the chopped vegetables and sauté for 4 to 5 minutes until just softened.
Reduce the heat slightly and pour the whisked eggs over the vegetables.
Let the eggs cook undisturbed until mostly set, about 3 to 4 minutes.
If using cheese, sprinkle it on top once the eggs are nearly cooked.
Gently fold the omelette in half and cook for another 1 to 2 minutes.
Remove from heat and serve immediately.
