How to Make It
Combine the tomatoes, onion and olive oil in a medium heavy saucepan and bring to a boil over moderate heat. Reduce the heat to moderately low and simmer, stirring occasionally, until the sauce has thickened but is still bright and fresh-tasting, about 30 minutes. Season to taste with salt and pepper. Remove from the heat.
Preheat the oven to 400°. Brush both sides of the eggplant slices with 3 tablespoons of the olive oil. Season with salt and pepper. Arrange the eggplant slices on 2 baking sheets and cover evenly with mozzarella. Bake, switching the position of the baking sheets halfway through, until the eggplant is tender, about 15 minutes.
While the eggplant roasts, heat 4 tablespoons of the olive oil and the garlic in a small saucepan over low heat until very fragrant (do not let the garlic brown), about 3 minutes.
Preheat the broiler. Brush the bread with the garlic oil and arrange on a baking sheet. Divide the eggplant slices evenly over the two halves of bread, then spoon about 2/3 cup tomato sauce over the eggplant (you will not use all of the sauce). Dot the sauce with the torn mozzarella and sprinkle the parmesan over the sandwiches. Season with pepper and drizzle the remaining 1 tablespoon olive oil over the sandwiches.
Broil the sandwiches until the cheese is bubbling and golden, 3 to 5 minutes. Cut each the sandwiches into 4 equal pieces and serve immediately.