Layer the eggplant slices in a colander, sprinkling each layer with the salt. Set aside to drain for at least 1 hour. Pat the eggplant dry with paper towels.
Preheat the oven to 375F. Using 1/4 c. of the olive oil, brush both sides of each eggplant slice. Arrange the slices in a single layer on 2 large baking sheets. Bake for 15 to 20 minutes, turning once, until the eggplant is tender when pierced with a fork but still holds its shape.
Remove from the oven; season with eggplant with the pepper. Cover half the eggplant with mozzarella. Finely chop the anchovies and basil together; sprinkle over the cheese. Cover with the remaining eggplant slices to form sandwiches.
In a medium bowl, beat the eggs with 2 teaspoons of water and 2 tea- spoons of the olive oil. Coat the eggplant sandwiches with the flour, dusting off any excess. Dip into the beaten egg, then coat the sand- wiches thoroughly with the bread crumbs, pressing gently to adhere.
In a large heavy skillet, heat the remaining oil over moderately high heat to 375F or until a small bread cube browns in about 1 minute. Fry the eggplant sandwiches in small batches until golden, 1 to 2 minutes per side. Remove with a slotted spoon and drain on paper towels. Arrange the sandwiches on a platter or plates and serve on their own or with Marinara Sauce, garnished with sprigs of fresh basil.
(The eggplant sanndwiches can be assembled and fried early in the day. Set aside on a cookie sheet at room temperature and reheat in a 400F oven for about 5 minutes just before serving.)