Preheat the oven to 180°c fan or 200°c conventional oven, 392°f, or 6 gas mark. Wash the eggplants, the tomatoes, and the basil leaves under cold running water. Chop the garlic cloves on a chopping board using a knife and set it aside. Trim the stem of the eggplants on a chopping board using a knife, and discard the stem. Lay the eggplant on its side and carefully slice it into rounds slice 1 cm/ 0.39 inch thick. Cut the round eggplant into small cubes and set it aside.
Take a baking tray and cover it with baking paper to prevent sticking. Add the eggplant cubes to the baking tray, spreading them out in a single layer. Add the garlic cloves to the tray, drizzle 6 tablespoons of oil over the eggplants, and season with salt and black pepper. Mix everything together, and ensuring that the eggplant cubes are well coated with the seasonings. Put the eggplant in the oven and roast them for 15 minutes.
Place the tomatoes on a chopping board and halve them using a knife. Take a medium frying pan and add the halved tomatoes, oil, garlic, and basil leaves to it. Mix everything together. Set the frying pan on medium heat and let the cook, stirring occasionally.
After 15 minutes, remove the eggplant from the oven and use a wooden spoon to flip them. Return the eggplant to the oven and allow it to roast for another 10 minutes. As the tomatoes start to soften, add the salt and mix everything. Using the wooden spoon, gently crush the tomatoes to create a sauce-like consistency. Let cook the sauce for 2 minutes, and once ready, set the side. Once the eggplants have achieved a nicely roasted golden color, carefully remove them from the oven and set them aside.
Set aside 33 gr of roasted eggplant for decoration. Add the rest of the roasted eggplants, 1 tablespoon of oil, and the water in a blender. Blend the eggplants at high speed for fews seconds until you have a creamy texture.
Bring a large pot with some salted water to boil. Once it starts to boil, add the casarecce pasta and cook for 9 minutes or until al dente. Stir often. In the meantime, add the eggplants pure in the tomato sauce and mix with a wooden spoon until combined.
Drain the pasta and set aside some pasta water. Turn the stove on medium heat and add the pasta to the sauce, the water, and a little grated cheese in a frying pan. Give a good stir until you get a cream sauce, but not too liquidy.
Just before serving the pasta, sprinkle the remaining roasted aubergines and some grated cheese. Serve immediately.