Preheat oven to 475 degrees. In a shallow bowl, lightly beat eggs with 1 teaspoon salt and 1/4 teaspoon pepper. Spread breadcrumbs in a pie plate or shallow bowl.
Oil a rimmed baking sheet. Dip eggplant rounds in egg, then dredge in breadcrumbs, turning to coat completely; transfer to prepared baking sheet. Bake (without turning) until golden and tender, 15 to 20 minutes.
Meanwhile, split bread lengthwise, and place cut side up on another baking sheet; press gently in centers to create a well. Layer both halves with tomato sauce, eggplant, and cheese. Bake until cheese is browned in spots, 6 to 8 minutes.