Toss eggplant and salt together in a bowl. Let rest for 20-30 minutes to let the water draw out. Transfer eggplant gently gently into a colander (but do not rinse), then squeeze lightly with a paper towel.
Heat the olive oil in a saute pan over medium heat; add the garlic and quickly cook for 30 seconds, taking care not to burn. Meanwhile, Bring a large pot of salt of water to a boil.
Add the eggplant to the saute pan and cook for 5-7 minutes until soft and slightly browned. Add the zucchini, and cook an additional 5 minutes, then add in the broth, pepper, oregano, cherry tomatoes and cook another 5 minutes until tomatoes are softened and mixture has thickened.
Add the rigatoni to the boiling water and cook until al dente.
Add the basil and balsamic vinegar to the eggplant mixture and remove from heat. Toss with the cooked pasta and season to taste, adding more salt/pepper if desired. Enjoy!