Bring a large pot of heavily salted water to a boil over high heat.
Meanwhile, heat oil in a large frying pan over medium-high heat. When it shimmers, add the onion and garlic and cook until just softened. Add eggplant, stir to coat in oil, then let cook, stirring rarely, until softened and golden brown, about 5 to 7 minutes. Remove half eggplant mixture and reserve.
Meanwhile, add the pasta to the boiling water and cook according to the package instructions.
Reduce heat to medium-low, add the tomatoes, cream, and half the basil, and let simmer, stirring occasionally, until flavors meld and sauce is slightly thickened, about 4 minutes.
Drain pasta and return to the pot off the heat. Pour sauce over top and stir until well coated. Add reserved eggplant, remaining basil, and mozzarella and mix until the cheese starts to soften. Serve immediately.