Heat the oven to 240C.
Put the aubergine cubes on a large oven tray lined with greaseproof paper, add three tablespoons of oil, half a teaspoon of salt and a good grind of pepper, and toss to coat. Roast for 30 minutes, stirring once halfway, until deeply browned and softened.
Meanwhile, prick the whole aubergines all over with a fork and ventilate your kitchen. Put a well-greased griddle pan on a high heat and, once smoking, lay in the aubergines and cook, turning as necessary, for 35 minutes, or until well charred all over, leave to cool slightly, then transfer to a bowl.
Toss the onion wedges, tomatoes and chilli in a bowl with a tablespoon of oil, then grill in the same pan for 10 minutes, turning the vegetables as necessary, until very well charred and softened. Transfer to a bowl, discarding the chilli stem. Once cool enough to handle, peel and discard the skin and stems of the charred aubergines (it’s OK if there’s still some skin attached) and add the flesh to the bowl with the charred vegetables – you should have roughly 320g aubergine flesh.
Put the tomato paste, paprika, three-quarters of the garlic and four tablespoons of oil in a small saucepan on a medium heat and cook for about six minutes, stirring occasionally, until the garlic is fragrant and the tomato paste has turned dark red. Transfer this and the vegetable mixture to a food processor, add three-quarters of a teaspoon of salt and a good grind of pepper and blitz until very smooth. Tip the puree into a large saute pan and set aside.
In a small bowl, whisk the tahini, remaining garlic, lemon juice, 70ml water and a pinch of salt until smooth.
Bring a pot of very well-salted water to a boil, add the pasta and cook for eight minutes, or until al dente, then drain the pasta and reserve 275ml of the cooking water.
Put the reserved pasta water and half the roast aubergine in the pan with the charred aubergine mixture and heat through on a medium-high heat. Add the drained pasta and stir to warm through for a couple of minutes. Toss the remaining roast aubergine with the parsley and the last three tablespoons of oil.
Transfer the pasta to a large serving platter with a lip, drizzle over half the tahini, then spoon over the aubergine and parsley mixture and serve with the extra tahini alongside.