Cook the pasta al dente (it should have a bite to it).
Cut the eggplant into 1 cm / ½ inch slices, then into 1 cm / ½ inch 'fries'. You can cook it right away or better, if you have time, sprinkle with a teaspoon of salt, wait 10-15 minutes, then dry thoroughly with paper towels. The salt extracts water from the eggplant, so it‘s easier and quicker to fry and less oil can be used.
Heat the oil on a large frying pan, spread the eggplant evenly, cook over high heat, without stirring, for about 3 minutes, then cook for 4 more minutes, stirring from time to time, until the eggplant is browned and tender. Transfer to a plate.
Reduce the heat under the pan, add the finely chopped garlic and dried oregano (and dried basil, if you‘re not using fresh leaves), cook for 30-60 seconds, stirring, then add butter, cook until melted.
Add the wine, stir until almost completely evaporated.
Add the canned tomatoes, break them up into smaller pieces with a spatula, cook over low heat for about 5 minutes, adding basil leaves at the end. Scrape all browned bits from the bottom of the pan with a spatula.
Blend the sauce until smooth, season with salt and pepper to taste (you can use a hand/immersion mixer to do this, but I would transfer the sauce into a high-rimmed bowl first, as it tends to splash when blended directly on the pan).
Add the cooked pasta, grated cheese and fried eggplant to the pan, mix together, season with salt and pepper to taste.
Serve sprinkled with basil leaves and grated cheese.