Line a large plate with paper towels. Put down a layer of eggplant slices, sprinkle generously with salt; add another layer of paper towels and another layer of eggplant and salt; repeat until you’ve layered the rest of the eggplant. Let sit for 20 minutes.
Put the flour and eggs in separate wide shallow bowls. In another wide bowl, toss the breadcrumbs with the thyme and 1/2 tsp. salt. Line a baking sheet with paper towels. Dredge the eggplant slices in the flour, dip in the egg, and then coat with the breadcrumbs, pressing down to pat the crumbs onto the eggplant, and put on the baking sheet.
Line another baking sheet with fresh paper towels. Pour enough oil into a large (12-inch) skillet or frying pan to measure about 1/2 inch deep and heat over medium heat until hot (if you dip a piece of eggplant into the oil, it will sizzle immediately). Working in batches, add as much eggplant as will fit in a single layer and fry, flipping once, until golden brown, 1 to 2 minutes per side. Transfer to the baking sheet. Repeat, frying the remaining eggplant and layering it between sheets of paper towel.
Position a rack in the center of the oven and heat the oven to 425°F. Arrange a layer of eggplant in a 9x13-inch baking dish. Top with 1 cup of the marinara and then cover with a third of the basil, mozzarella, and Grana Padano. Repeat with two more layers of the remaining eggplant, marinara, basil, mozzarella, and Grana Padano.
Bake until the cheese melts and browns and the sauce bubbles around the edges, 25 to 30 minutes (cover with foil if the top browns too quickly). Let cool for a couple minutes and serve.