Put the soup in a medium pot, add in the Parmesan rind and bring to a slight simmer.
Set up a standard breading station with the flour, eggs and breadcrumbs in separate shallow bowls. Lightly season each station with salt and pepper. In batches and using a spider or slotted spoon, dredge each eggplant cube in flour and shake off the excess; dip in egg and let the excess drip off; and then coat in breadcrumbs. Set aside on a wire rack.
Heat 1/2 inch of oil in 2 large straight-sided saute pans over medium heat. Working in small batches, fry the eggplant pieces, turning once, until golden brown, about 4 to 5 minutes a side.
Preheat the oven to broil. Ladle the soup into individual ovenproof crocks on a parchment-lined baking sheet. Cover each crock with 2 slices of mozzarella. Broil until golden brown and bubbly. Top each crock with several fried eggplant cubes and some basil chiffonade.