Heat pan on low-medium heat and add oil and garlic. After 3 minutes add the chopped tomatoes. As the sauce begins to simmer add the tomato puree and stir it in, turning the heat up. Add the sugar and salt to taste once the sauce has thickened.
Slice the aubergines into thin discs and pat them dry with kitchen roll to absorb the bitterness. Grill and turn over when the slices colour. When the aubergines are lightly toasted around the edges, take out and mix into the tomato sauce.
Spoon 1/3 of the mixture into a baking dish and smooth evenly. Add half of the mozzarella. Spoon another third into the baking dish and cover again with half of the mozzarella. Spoon the final third into the dish and cover with grated Parmesan.