Cut the eggplant into 4 quarters lengthwise. If they've got seedy, fluffy centers, remove them and chuck them away. Then cut the eggplants across the length, into finger-sized pieces or chunks.
Get a large pan nice and hot and add a little oil. Fry the eggplants in two batches, adding a little extra oil if you need to.
Give the eggplants a toss so the oil coats every single piece of the eggplant.
Using a pair of tongs, turn the pieces of eggplant until golden on all sides. Remove to a plate and do the same with the next batch.
When the eggplants are all cooked, add the first batch back to the pan add the dried red chili.
Turn the heat down to medium and add a little oil, the garlic, and the basil stems. Stir so everything gets evenly cooked, then add a swig of white wine vinegar and the cans or fresh tomatoes.
Simmer for 10 to 15 minutes, then taste and correct the seasoning.
Tear up half the basil leaves, add to the sauce, and toss around.
Put the spaghetti into a pan of salted boiling water and cook according to the package instructions. When it's done, drain, reserving a little of the water, and put it back into the pan.
Add the sauce and a little of the reserved cooking water and toss together then back on the heat.
Taste, and adjusting the seasoning and divide between your plates by twirling the pasta into a ladle for each portion. Any sauce left in the pan can be spooned over the top. Sprinkle with the remaining basil.