Bring a large pan of water to the boil for the pasta.
Pour enough oil into a deep, medium-sized frying pan for it to come 2.5cm up the sides and heat until hot. Working in batches, fry the diced vegetables in the oil until soft and golden, then blot on a kitchen towel, season with salt and keep warm. Tip the oil from the pan.
Plunge the tomatoes into the almost boiling water for a minute, then lift them out with a slotted spoon and refresh under cold water, at which point the skins should slip off. Roughly chop the tomatoes.
Put the frying pan back on the heat with four tablespoons of new oil and the garlic. Once the garlic is fragrant, add the chopped tomatoes and a pinch of salt and cook until soft and saucey – about 10 minutes.
Once the water is boiling, add salt, stir, then add the pasta and cook until al dente. Once the pasta is ready, drain, tip into the tomato pan and toss.
Tip the pasta and sauce into a large bowl, add the fried vegetables, Parmesan, mozzarella and ripped basil, toss thoroughly and serve.