In a shallow bowl, beat the eggs with salt. Spread the panko in a shallow pie plate.
Oil a baking sheet. Dip the eggplant in egg, then panko; transfer to the baking sheet. Drizzle the eggplant with a bit more oil (this helps make them extra crispy). Bake (without turning) at 475F until golden and tender, 15 to 20 minutes. Alternatively, you could just roast the eggplant with oil and salt (no dredging needed).
Cut the bread lengthwise. Remove a bit of the bread so that the filling has somewhere to live (I'd recommend this bit of bread to make breadcrumbs for another day). Layer both halves with sauce, eggplant and cheeses. Bake until cheese is browned in spots, 6 to 8 minutes.
Cut the eggplant parmesan melts into slices (or just caveman it and eat whole). Sprinkle the basil on top and serve with extra marinara on the side.
You actually don’t need to serve these on bread, if you don’t want to. You can omit it and layer the marinara, cheese and basil on a base of eggplant. Just make sure that you dredge the eggplant in egg + panko (instead of only roasting it), since it helps add more stability to the eggplant.