Heat 1 tablespoon olive oil in a large pot over medium-high heat. Saute eggplants, red onion, mushrooms, and garlic until softened, 8 to 10 minutes.
Heat remaining 1 tablespoon olive oil in a skillet over medium-high heat. Saute tomatoes until juicy and tender, about 6 minutes. Transfer tomatoes to the pot.
Cook and stir ground beef in the same skillet until browned and crumbly, 5 to 7 minutes. Transfer to the pot; add pasta sauce, tomato sauce, pizza sauce, sugar, spaghetti sauce mix, salt, and pepper. Stir and simmer until flavors are well blended, about 10 minutes.