First, heat 2 to 3 tablespoons of olive oil in a big heavy nonstick skillet over medium flame. At the same time, start a pot of water to cook the pasta.
Work in two or three batches, drizzling in more oil as needed. Sauté the eggplant until it is golden on both flat sides. When it’s all sautéed, add it all back into the pan.
Pour in the tomatoes, add the garlic, red pepper, herbs and vinegar and sprinkle with a little salt. Stir together, then simmer for about 15 minutes or so, stirring now and then.
Meanwhile, cook the pasta until it is al dente. Drain it, reserving some of the cooking water.
When the sauce is nicely cooked together, add the drained pasta and stir and toss everything together. The idea is to evenly distribute the sauce. You don’t want pasta swimming in sauce—the sauce should coat the pasta and be gently absorbed by it. If the sauce seems too thick or you want to extend it a bit, add some of pasta water, a few tablespoons at a time.
Plate individually, making sure everyone gets nice chunks of eggplant. Grate some cheese on top—not much! Just a grace note. It’s ready.