Prep the breading work area. Measure flour and put on a plate. Then measure the breadcrumbs and put on a second plate; add salt and pepper and mix well. Beat 3 eggs in a large, shallow bowl and place between the two plates.
Trim the top and bottom of the eggplant. Slice about ⅜" rounds, or just larger than ¼" rounds.
Preheat the oil in a large frying pan over medium, medium-high heat.
Using one hand, move each slice of eggplant through the flour, coating well. Then dip into the egg, coating well again. Finally, gently press each side into the bread crumbs to ensure it's well-coated.
Using a slotted turner (or tongs), gently place battered eggplant slices into the oil in a single layer. You will have to do a few batches. Fry on each side without disturbing for about 3 minutes per side, until golden brown. Transfer to a paper-towel-lined plate. Repeat until all slices are fried.
Preheat the oven to 400ºF. While the slices fry, slice the tomatoes into the same number of slices as you have eggplants. Also prepare the sliced mozzarella. Once the slices are fried, place on a lightly oiled sheet pan (half-size is fine) and top with the sliced tomatoes and then the sliced mozzarella.
Bake the slices at 400ºF for 3-5 minutes, until the mozzarella just barely starts to melt. While that bakes, slice the basil leaves.
Remove and top with a pinch of red pepper flakes, a pinch of a flaky salt and the sliced basil leaves.