Preheat the oven to 190°C (375°F/gas 5). Trim the tops from the aubergines and slice lengthways as thinly as possible, making sure there are no holes. Season to taste with salt and fry a few at a time in a dry non-stick frying pan (skillet). Leave to cool.
Peel and finely chop the garlic. Heat the oil in a saucepan and sauté the garlic over a low heat. Add the tomatoes and season with salt. Put the tomato sauce in an ovenproof dish or casserole.
For the filling, rinse the basil, pat dry, pluck the leaves, and cut into thin strips. In a bowl, mix the mascarpone, ricotta, and Parmesan with the basil and egg yolk. Season with salt and pepper.
Spread 1 tablespoon of filling over each aubergine slice, roll into small parcels, and place in the tomato sauce. Tear the mozzarella into small pieces and spread over the parcels. Bake the involtini for 35 minutes until the cheese turns golden brown. Serve warm with the ciabatta.