Halve peppers, remove seeds and ribs and cut into bite-sized pieces. Peel and finely chop shallot and garlic. Rinse zucchini and cut into 1 cm cubes (approximately 1/2-inch cubes).
Whisk eggs with cream and season with salt and pepper. Pour half of the mixture into the pan and cook until golden. In a second pan, sauté garlic and onion in hot oil. Add zucchini cubes and sauté. Add pepper pieces and sauté briefly. Season with salt, pepper and lime juice. Slide omelette onto a plate, flip onto a second plate and slide back into the pan. Cook 2 minutes. Transfer to a preheated dish, cover with half the zucchini and pepper pieces, sprinkle with crumbled feta cheese and serve garnished with basil. Cook the second omelette in the same manner with the remaining ingredients.