Chop the eggplant into rough 3/4 inch chunks. Place into a colander in the sink, sprinkle with sea salt to draw out the moisture, then set aside for about 20 minutes.
Peel and finely slice the garlic. Pick the basil leaves and finely slice the stalks. Rinse the eggplant and pat dry with paper towels. Place into a large bowl with the oregano, chile flakes, a splash of olive oil, and a pinch of sea salt and black pepper. Toss together well.
Drizzle a splash of olive oil into a large frying pan over medium heat. Once hot, add the eggplant in a single layer, and fry for 5 to 8 minutes, or until softened and golden, stirring occasionally—you may need to do this in batches.
Add another splash of olive oil, followed by the garlic, capers, and basil stalks, then cook for a further 2 minutes, or until golden. Stir in the vinegar and the tomatoes, breaking them up with the back of a spoon. Reduce the heat to low, and simmer gently for 15 to 20 minutes, or until thick and glossy.
Cook the pasta in a pan of boiling salted water until al dente, it should have bite and firmness to it. Drain pasta reserving a cupful of the cooking water, then add a good splash of the reserved water to the sauce.
Finely grate the cheese and tear most of the reserved basil leaves. Add a glug of extra virgin olive oil, then season to taste. Add pasta to the sauce and toss well, adding an extra splash of the reserved cooking water to loosen, if needed.
Divide between bowls, grate the remaining cheese over pasta, and finish with the remaining basil scattered on top.