Clean and wash the zucchini and cut into spaghetti with a spiral slicer. Season with 1 tsp salt. Preheat oven (electric cooker: 200 °C/circulating air: 180 °C/gas: see manufacturer). Grate cheese.
Squeeze the zucchini in a sieve, mix with tomatoes and half of the cheese and season with pepper. Put them into an ovenproof dish (approx. 24 cm Ø). Form 4 hollows for the eggs. Beat the eggs one after the other and distribute them in the hollows. Sprinkle the rest of the cheese onto the casserole. Bake in a hot oven for about 35 minutes.