Heat 1 tbsp of olive oil in a skillet over medium heat. Add the diced zucchini, eggplant, red bell pepper, and tomato. Cook until tender, about 10 minutes.
Add the minced garlic and cook for another 2 minutes. Season with salt and black pepper to taste. Remove from skillet and set aside.
In a mixing bowl, beat the eggs with a pinch of salt and pepper.
Heat the remaining 1 tbsp of olive oil in the skillet over medium heat. Pour in the beaten eggs and let them cook until they start to set.
Add the cooked vegetables on one half of the omelette. Fold the other half over the vegetables and cook for another 2-3 minutes until the eggs are fully set.
Slide the omelette onto a plate, garnish with chopped fresh basil, and serve hot.
