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Heat the oil in a large frying pan. Add the onion, pepper, garlic and rosemary, then cook for 5 mins, stirring frequently, until the onion has softened. Add the aubergine and courgettes, then cook for 2 mins more.
Add the tomatoes, then fill the can with water, swirl it around and tip into the pan. Bring to the boil, cover, then simmer for 40 mins, uncovering after 20 mins, until reduced and pulpy.
Stir the vinegar into the ratatouille, then make 4 spaces for the eggs. Crack an egg into each hole and season with black pepper. Cover, then cook for 2-5 mins until set as softly or firmly as you like. Scatter over the basil and serve with some crusty bread to mop up the juices.