Sprinkle the cut eggplant with salt and allow to sit for 15 minutes to draw out the moisture.
Meanwhile, in a shallow dish, mix whole-wheat panko crumbs, breadcrumbs, Parmesan cheese, and a pinch of salt and pepper.
In a second shallow dish, stir the eggs with a touch of water and a bit of salt and pepper.
In a third shallow dish, mix all-purpose flour and a touch of salt.
Pat the eggplant slices with paper towels to dry and dredge each slice into the seasoned flour, then into the egg mixture, and finally into the seasoned breadcrumb mixture.
Add olive oil to a large skillet over medium heat, and brown the coated eggplant slices (in batches) on both sides until golden brown approximately 45-50 seconds per side.
Remove the eggplant to a baking sheet fitted with a wire rack, and season them immediately with a light touch of salt and pepper. Keep warm in a low (200-degree oven).
Meanwhile, sauté the bell pepper in any remaining oil, and in the same skillet as the eggplant slices.
Season the bell pepper lightly with salt and pepper and cook, stirring occasionally, for approximately 3 minutes, or until soft.
Meanwhile, slice the tomato and season it lightly with salt and pepper.
Toast the bread, and assemble the sandwich by laying lettuce leaves (I used butter lettuce) on the bottom and top with a few slices of fried eggplant, the sauteed bell pepper, the seasoned tomato, and the top slice of toast that has been spread mayonnaise.
Slice and serve immediately.