Preheat the oven to 425 degrees . Lightly spray a baking sheet with cooking spray. In a shallow bowl, beat the eggs and olive oil. In another shallow bowl, combine the breadcrumbs and 1/2 cup parmesan. Working with 1 slice at a time, dip the eggplant in the egg mixture to coat, then coat with the breadcrumb mixture. Arrange in a single layer on the prepared baking sheet. Bake, turning once, until golden, about 25 minutes.
Position a rack in the upper third of the oven and preheat to 350 degrees . Trim the ends of the semolina loaves and halve lengthwise; scoop out some of the insides and discard. In a medium bowl, combine the mozzarella and muenster. Spread 1/2 cup tomato sauce on each loaf bottom, then sprinkle each with 2 tablespoons parmesan. Top with one-quarter of the baked eggplant and one-quarter of the cheese mixture. Repeat the layering, starting with the tomato sauce. Cover with the loaf tops.
Wrap the subs in heavy-duty foil, place on a baking sheet and bake until heated through, 30 minutes. Let cool for 5 minutes before slicing.