Put a pot of water on to boil and add 1 tsp oil and salt.
Heat oil in a large non stick skillet over medium heat. Add eggplant and cook, stirring occasionally, until just softened, about 5 minutes.
Add garlic and cook, stirring, until fragrant, 30 seconds to 1 minute.
Add tomatoes, olives, vinegar, capers, salt, pepper and crushed red pepper (if using) and cook, stirring, until the tomatoes begin to break down, 5 to 7 minutes more.
Meanwhile, cook pasta in boiling water until just tender, about 6 minutes or according to package directions.
Drain and divide the pasta on a serving plate.
Spoon the sauce over the pasta and garnish with slivers of cheese and basil on top.