A little over an hour before you start cooking the eggplants, rinse and pat them dry. Slice off the root and stem ends. Peel the eggplants using a small knife (cut the eggplant in half the short way, stand up each half, and slice off the skin from top to bottom.) Slice the eggplants into rounds ¼-inch-to-⅓ inch thick.
To draw out moisture from the eggplants so they won't be soggy and will have better flavor, place a layer of eggplants in a colander placed over a sheet pan. Sprinkle salt on the eggplants, then add another layer of the slices. Salt those, then weigh the eggplants down with a round baking dish or pot. Let them sit for an hour.
Make the Tomato Sauce
While the salted eggplants are resting, make the sauce. In a medium pot or 12-inch skillet, add the crushed tomatoes, olive oil, seasonings and basil. Stir to combine and heat on medium-high, until it comes to a boil. Lower the heat to a simmer and cook the sauce for 10 minutes, stirring occasionally so it doesn't stick. Turn off the heat when it's done. The sauce can stay at room temperature for up to two hours.
Batter & Fry the Eggplants
After the eggplants have rested for an hour, use paper towels to wipe off the moisture and salt from the slices. If there are lots of seeds, scrape out some of them to prevent bitterness.
Add the flour to a gallon-sized resealable plastic bag, if you have one, or else add the flour to a dinner plate. Stir in ⅓ teaspoon pepper and ¼ teaspoon salt.
Add two eggs to a soup dish and beat the eggs with a fork.
Set up an assembly line from left to right with the sliced eggplants, the flour, the eggs and a large platter. Add five or six eggplant slices to the flour mixture and coat both sides with flour. (If using a bag, just hold it closed and shake it.)
Use a clean fork to transfer a couple of eggplant slices to the beaten eggs. Use another fork designated for the eggs to flip the eggplant slices, coating both sides with the eggs. Transfer the battered eggplant slices to the platter and continue with the rest of the eggplants.
As the beaten eggs get thick with flour and are almost gone, rinse out the bowl and add a couple more eggs, as needed.
To fry the eggplant slices (see notes if you want to bake them instead), heat the oil in a frying pan over medium-high heat. (You can use two pans, if you wish, to make it go faster.) When the oil is hot, add a single layer of sliced eggplants and cook the first side for 3-4 minutes, until golden brown. Flip the eggplants and cook the second side for two minutes, or until golden brown.
Drain the fried eggplants on a baking rack placed over a sheet pan, or on a sheet pan lined with paper towels. Continue frying the eggplants in batches.
Assemble & Bake
Preheat the oven to 375 degrees F. Choose either a square 8x8 pan for four layers of Eggplant Parmigiana (recommended) or a rectangular 9x13 baking pan to make two layers.
To assemble the eggplant parm, cover the bottom of your pan with a layer of sauce. Blot the eggplants with paper towels to absorb the oil. Add a single layer of eggplants. Sprinkle them with pepper. For an 8x8 pan, sprinkle on one tablespoon of Parmesan per layer. For a 9x13 pan, sprinkle on two tablespoons of Parmesan per layer.
Dot the eggplants with some sauce. Scatter some torn basil leaves on top. Add a layer of provolone slices, with a little bit of sharp provolone chunks scattered in the gaps.
Add another layer of eggplants, sprinkle on pepper and Parmesan, dot with sauce and basil leaves, top with provolone slices and add scattered sharp provolone in the gaps. (If using an 8x8 pan, continue making two more layers.)
Top the Eggplant Parmigiana with more sauce dotted around, and sprinkle with Parmesan.
Bake, uncovered, for 35 minutes, or until it's just getting golden brown on top.
Let it rest for five minutes before slicing. Serve with extra sauce, if desired.
Store leftover eggplant Parmesan in the refrigerator for up to four days. Store leftover sauce for up to five days in the refrigerator, or freeze the sauce for longer storage. See notes for how to freeze Eggplant Parmigiana before baking it.
Notes
When making eggplant Parmigiana with flour and egg instead of bread crumbs, it's best to fry the eggplant slices.
If you try to bake the eggplant after coating it with flour and egg, the slices will stick to the pan, since there are no bread crumbs in this recipe. Here is how to do it though: Place the battered slices on a greased baking sheet (don't use foil and don't use a baking rack, because they'll stick more.) Bake at 450 degrees F for 10 minutes on the first side. Use a metal spatula to flip them over. Bake the second side for 5-7 minutes. Assemble as directed in the recipe.
If you don't mind using bread crumbs, you can bake the eggplant slices using this breaded eggplant recipe instead.
You can freeze Eggplant Parmigiana after assembling it, without baking it first. Cook the eggplant slices and sauce as directed, then layer everything in a pan with cheese. Wrap the pan well with plastic wrap, then foil. Freeze the assembled Eggplant Parmigiana for up to three months. Then, let it thaw overnight in the refrigerator and bake as directed.