Preheat the grill to medium high. Grill the peppers cut-side down for about 15-20 minutes until the skins are fully blackened. Carefully transfer to a bowl and cover tightly with cling film. Set aside for 10 minutes to allow the steam to loosen the skins.
Meanwhile, heat a griddle pan until hot and brush the aubergine slices with 2 tablespoons of the oil. Cook in batches on a low heat for about 5 minutes on each side, or until chargrilled and just tender. Set aside.
Preheat the oven to 180°C, fan 170°C, gas 4. Remove the peppers from the bowl, being careful to avoid the hot steam. Peel the skin from the peppers and discard.
In a separate pan, heat the remaining oil and gently fry the garlic for 2-3 minutes. Stir in the arrabbiata sauce, 150ml water and the basil. Bring to the boil, season and remove from the heat.
Arrange a layer of peppers and aubergines on the bottom of a shallow 1.5 litre ovenproof dish. Pour over some of the sauce and sprinkle with a little parmesan. Repeat with the remaining ingredients, then top with the mozzarella and a final sprinkle of parmesan.
Bake for half an hour, until bubbling. Serve scattered with fresh basil.