Eggplant is full of water. You need to draw that water out for good frying results. About an hour or two before you are going to be cooking, slice the eggplant into ½" slices. Brush both sides with lemon juice and place on 2 layers of paper towel. Generously salt one side of the eggplant. Let sit for one hour. It will have water beads on top. Dab those off with a paper towel, turn the eggplant over, salt and let the other side sit. Dab off the moisture. Brush off any visible salt.
Slice the onion and fresh mozzarella cheese. Each should be about ½" thick. Set aside.
Lightly butter the Brioche buns and set aside.
Tear off a few fresh basil leaves and set aside.
Beat eggs in a shallow dish with a fork. Add 1 TBS water, stir and set aside.
Mix the flour, Panko breads crumbs, salt, pepper, and half the grated Parmigiana in a shallow dish. Pie pans work great.
Pour oil ito a frying pan to 1" depth. Heat oil over medium heat. Save some oil for changing out between each fried item.
Starting with the eggplant, dip into the eggwash until coated, then dredge in the flour mixture, coating both sides. Place the eggplant into the hot oil. It should start browning but not smoke. Monitor the heat clsoely as it burns quickly. Turn the eggplant over and fry on the other side until golden brown. Place the eggplant on paper towels, and lightly sprinkle with salt. Pour out the used oil.
Add fresh oil to the pan and heat over medium. Dredge the sliced cheese through the egg wash then the flour. Fry, turning once, until golden brown on both sides. Place on paper towels and lightly sprinkle with salt. Pour out the used oil.
Add fresh oil to the pan and heat over medium. Dredge the onion rings through the egg wash then the flour. Fry, turning once, until golden brown on both sides. Place on paper towels and lightly sprinkle with salt.
Broil the buttered buns until golden brown on top. Watch carefully as they burn quickly.
Spread marinara sauce on both buns and layer the fried eggplant, onion and mozzarella on the sandwich. Sprinkle grated parmesan on the egglant, put the top bun on and enjoy piping hot!