Cut the ends off each eggplant and slice a small piece off one side to give you a flat side to rest the eggplant on. With the flat side of each eggplant down so it doesn't roll, slice them each lengthwise into four thick slices each (eight slices total). Season the slices with salt and freshly ground black pepper and coat each of them with the ingredients in your pans -- first in the flour, then in the egg, then in the breadcrumb mixture, making sure to thoroughly coat the surface of each slice with each ingredient.
Once all of your slices are breaded, carefully lay them into the hot oil and fry them until golden brown on both sides, 2-3 minutes per side. (You will need to work in batches to finish cooking all of the eggplant.) As they finish shallow frying, transfer them to a cooling rack set over a baking sheet.
When all the eggplant is fried, transfer the baking sheet to the oven to finish cooking through, about 10-12 minutes, until they're tender when you poke them. Once they're out of the oven, fire up your broiler.
While the eggplant steaks finish cooking in the oven, place a small saucepot over medium-high heat with the can of San Marzano tomatoes. Mash up the tomatoes with a potato masher or wooden spoon. Once the tomatoes come up to a bubble, turn off the heat and stir in the pesto. Season the sauce with salt and freshly ground black pepper.
To finish the dish, place one of the eggplant steaks onto an oven-proof serving plate. Ladle a little sauce over top of it, then set another steak on the plate, slightly overlapping the first. Ladle some more sauce over the top steak and sprinkle some provolone and Parmigiano over top. Place the plate under the broiler to melt and slightly brown the cheese, about 1 minute. Serve immediately, garnished with parsley.