Salt eggplant or tomatoes and drain on paper towels or a dishtowel for 20 minutes, turning once.
For the sauce: Heat a saucepot over medium heat with the butter. When it foams, add garlic and stir 1 minute. Add onion and tomatoes, crushing up tomatoes a bit; stir in basil and a little salt. Simmer 20 minutes then remove onion.
Sandwich mozzarella slices between eggplant or tomatoes. Coat sandwiches in flour, egg then a mixture of breadcrumbs, grated cheese, cornmeal, granulated onion and garlic, and parsley.
Heat oil over medium to medium-high heat. Fry stuffed eggplant or tomato sandwiches about 3 minutes on each side until golden. Serve hot with sauce alongside.