Grate the zucchini, sprinkle with a little salt and drain thoroughly in a sieve.
Grate the potatoes, soak briefly in water, then drain and press out excess liquid.
Chop the onion and grate the carrot, then sauté them gently in vegetable oil until soft.
Add the drained potatoes to the pan and cook for about ten minutes, stirring regularly.
Add the drained zucchini to the pan and cook for a further five minutes, stirring often.
Beat the eggs in a bowl, then add salt, black pepper, oregano, basil, smoked paprika and flour, mixing to form a smooth batter.
Combine the warm vegetable mixture with the egg batter, stirring until evenly coated.
Heat olive oil in a clean frying pan, pour in the mixture and cook over medium heat for about ten minutes until the underside is golden.
Flip the skillet bake onto a plate and return it to the pan, then top with tomato slices and grated cheese.
Cover with a lid and cook for another ten minutes until the cheese melts, the tomato softens and the centre is fully set, then serve hot.