Heat EVOO in a saucepot over medium heat, add onions and cook 8-10 minutes. Add garlic and cook 2 minutes more. Add tomatoes and sauce or purée, some torn basil, salt and pepper. Reduce heat and simmer 25-30 minutes, stirring occasionally and breaking up tomatoes.
Meanwhile, season the eggplant slices with salt and let drain in a colander 30 minutes.
Preheat oven to 375˚F.
Coat eggplant slices in flour, the beaten eggs, then breadcrumbs mixed with 3/4 cup (3 handfuls) of cheese and parsley.