Heat the olive oil in a large saucepan and cook the eggplant for 5 mins until starting to brown and soften.
Add the onion, garlic, chili and oregano, and cook for just a few minutes.
Add the tomatoes, balsamic vinegar and about 1 cup water.
Reduce heat and simmer gently for about 20 mins, until the tomatoes are reduced and really softened, and the sauce is thickened.
Meanwhile, bring a large pan of water to the boil and cook the tagliolini following package instructions.
Drain the pasta and return to the pan.
Add the sauce and toss well into the pasta with the basil.
Serve with the grated pecorino.