Trim the top and bottom of the eggplant. Cut the eggplant into 1-inch / 2.5cm cubes and transfer them to a colander. Salt the eggplant generously and allow it to sit for 20 minutes. Rinse the eggplant well, then pat thoroughly dry with a tea towel or paper towel.
Bring a pot of salted water to a boil. Add the pasta and cook according to package instructions. Drain the pasta, reserving 1/2 cup pasta cooking water.
While the water boils and pasta cooks, heat the oil in a large, deep skillet over medium heat. Add the eggplant and sauté, stirring often, until it's browning and tender, about 8-10 minutes. Add the zucchini and cook for another 5 minutes, stirring now and then; add the garlic and cook for 1 minute more, stirring constantly.
Add the diced tomatoes, tomato sauce, sugar, oregano, basil, and thyme. Heat through. Test for seasoning. Add salt and pepper to taste. Add the white beans and heat the whole mixture through.
Add the pasta and reserved cooking water to the skillet. Bring the mixture to a simmer and simmer, uncovered, for 5 minutes. Serve.