A little over an hour before you start cooking your 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, 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.
While the salted eggplants are resting, make your sauce, if needed. In a medium pot or 12-inch skillet, add your 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.
After your 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 your 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 your sliced eggplants, the flour, the eggs and a large platter. Add five or six eggplant slices to your 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 eggplant slices to your beaten eggs. Use another fork designated for the eggs to flip your eggplant slices, coating both sides with the eggs. Transfer the battered eggplants slices to your platter and continue with the rest of your eggplants.
As your 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 your 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 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 your eggplants in batches.
Preheat your oven to 375 degrees F. Choose either a 9x13 baking pan for two layers of Eggplant Parmigiana, or an 8x8 pan for four layers.
To assemble your eggplant parm, cover the bottom of your pan with a layer of sauce. Blot your eggplants with paper towels to absorb the oil. Add a single layer of eggplants. Sprinkle them with pepper. For a 9x13 pan, sprinkle on two tablespoons of Parmesan per layer. For an 8x8 pan, sprinkle on one tablespoon 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 sharp provolone scattered in the gaps.
Add another layer of eggplants, sprinkle on pepper and Parmesan, dot with sauce and basil leaves, and top with provolone slices and scattered sharp provolone. (Make two layers for your 9x13 pan, and four layers if using an 8x8.)
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 it for longer storage.
When buying eggplants, choose skinnier ones if possible. They should have fewer seeds. Make sure the eggplants are firm and not bruised. They should have green tops, not brown. If the ones on display look bad, ask a produce employee if there are any more in the back. (He or she can bring out a box and let you pick the ones you want.) Cook the eggplants within two days of purchasing them.You can bake the battered eggplant slices, instead of frying them, but they will stick to the pan, since there are no bread crumbs in this recipe. 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.