1. Preheat your oven to 180°C (350°F). Meanwhile, slice the eggplants (using a mandoline makes it easier) and place them on a baking sheet. Brush with olive oil and sprinkle with salt. Bake for 10 minutes. Once out of the oven, cut into large pieces.
2. Meanwhile, dice the tomatoes and slice the zucchini. Peel and finely chop the onion. Peel and press the garlic cloves. Chop the basil.
3. Sauté the onion in a pan with a little olive oil, then add the tomatoes (diced, crushed, and tomato paste), zucchini, eggplants, garlic, paprika, and sugar. Season with salt and pepper and mix well. Bring to a simmer and let cook for about ten minutes, covered.
4. After this time, create 4 wells in the sauce and crack the eggs into them. Cover and let cook for 3-4 minutes, until the whites are cooked and the yolks are still runny. Serve hot with slices of toasted bread.