In a bowl, whisk together the eggs until well beaten. Season with salt and pepper.
Heat the oil or butter in a skillet over medium heat.
Add the diced vegetables to the skillet and sauté for 2-3 minutes until softened.
Pour the beaten eggs into the skillet, tilting the pan to spread them evenly over the vegetables.
Cook for 2-3 minutes, lifting the edges of the omelette with a spatula to let the uncooked egg flow underneath.
Once the bottom is set and the top is still slightly runny, sprinkle shredded cheese over one half of the omelette if desired.
Carefully fold the omelette in half with a spatula and cook for another 1-2 minutes until the cheese is melted and the omelette is cooked through.
Slide the omelette onto a plate and garnish with fresh herbs if desired.
Serve hot and enjoy your Vegetable Omelette!