Bring a large pot of water to a boil over high heat. Once boiling, add salt and the penne and cook the pasta until al dente according to package directions.
Preheat a skillet over medium-high heat. Add the onions and garlic and cook until soft, about 5 minutes.
While the onions and garlic are cooking, scoop the eggplant flesh from the skin and mash with a fork in a bowl. Add the mashed eggplant to the skillet with the onions and garlic. Season with salt and pepper. Add the crushed tomatoes and the torn basil. Add the penne to the skillet along with the Parmigiano Reggiano and mix thoroughly to combine.