Salt eggplants all over with 1 tablespoon kosher salt. Layer in a large colander set in the sink. Lay a plate over the eggplant and weight the top with cans to help press out excess liquid. Let drain about ½ hour, then rinse and pat dry.
Preheat oven to 375 degrees F. In a large shallow bowl, toss together the breadcrumbs, 2 cups of the grated cheese and 1 cup of the olive oil. Season with ½ teaspoon salt. In another shallow bowl, beat the eggs and milk with a pinch of salt. Spread the flour on a plate.
Dredge the eggplant slices in flour, egg, then breadcrumbs, pressing in the crumbs to make sure they adhere. Lay the eggplant slices on parchment lined sheet pans, without touching. Bake eggplant, rotating the sheet pans halfway through baking, until cooked through and crumbs are crisp and golden, about 25 minutes. Let cool slightly.
Meanwhile, in a large skillet, heat remaining 2 tablespoons olive oil over medium-high heat. Add smashed garlic and sauté until just golden, about 1 to 2 minutes. Add the spinach with any water clinging to the leaves, season with remaining ½ teaspoon salt, cover and cook until wilted, about 3 to 4 minutes. Check occasionally to make sure the bottom of the pan is not dry, adding water a tablespoon at a time if necessary. Once the spinach is wilted, uncover and cook until spinach is tender and excess water is gone, about 4 minutes.
To assemble the eggplant, spread ¾ cup of the marinara sauce in the bottom of a 10-by-15-inch baking dish. Add half of the baked eggplant, in an even layer. Spread with 1 cup marinara. Sprinkle with ½ cup grated Grana Padano. Sprinkle with half the shredded mozzarella. Spread all of the spinach in one layer. Spread with 2 more cups marinara. Sprinkle with the remaining grated mozzarella and ½ cup grated Grana Padano. Top with an even layer of the remaining eggplant. Spread remaining sauce on top and sprinkle with remaining grated Grana Padano. Tent the baking dish with foil, so it is not touching the cheese and bake until bubbly, about 30 minutes. Uncover and bake until cheese is browned and crusty and sauce is bubbling all over, another 15 minutes. Let cool and set 5 to 10 minutes before cutting and serving.