Preheat oven to 375ºF. Peel the Eggplant. (If it is just picked, you may want to leave the skin on.) Cut it into half inch rounds. Very lightly oil two baking sheets with the olive oil.
Add a little salt and pepper to the flour in a bowl. In a second bowl, fork stir the eggs. Put the panko crumbs in a third bowl. (If you don’t have panko crumbs, you can use herbed bread crumbs or a combination of panko and herbed bread crumbs.) Dredge each Eggplant slice in the flour, tapping off any excess. Dip each Eggplant slice in the egg wash, and then the panko crumbs, pressing to coat evenly and lightly. Place the breaded Eggplant slices on the oiled baking sheets, spreading them out evenly. Bake at 375ºF until just golden, about 20 minutes. Flip the slices over and bake for another 15 minutes. Remove from the oven and set aside.
Turn the oven down to 350ºF. Slice the mozzarella cheese into 1/2 rounds and cut into narrow matchstick pieces (easier than grating). Grate the Fontina cheese. Finely scissor-cut the Basil into narrow slivers. Slowly heat the Tomato sauce over low heat.
Spread a little bit of the warm Tomato sauce on the bottom of a 9 x 13 inch baking dish. Arrange a single layer of the oven-baked Eggplant in the baking dish, positioning them closely together. Spread a thin layer of Tomato sauce over the Eggplant. Lightly scatter half of the fine Basil slivers over the sauce. Evenly scatter half of the mozzarella and Fontina cheeses over the top. Drizzle Tomato sauce lightly over the surface. Repeat with another layer of Eggplant rounds, Tomato sauce, Basil and mozzarella and Fontina cheeses. Top with grated Parmesan. Bake at 350ºF for 20 minutes until bubbling hot. Remove from oven. Let it rest for 5 minutes to set a little bit before serving.