2 medium eggplant, peeled and cut into 1/4-inch slices
1/2 cup olive oil
1 container (15 ounces) whole-milk ricotta cheese
1/3 cup plus 1/4 cup grated Parmesan cheese, divided
2 tablespoons lemon juice
2 teaspoons dried parsley flakes, divided
1 teaspoon grated lemon zest
1/2 teaspoon kosher salt
2 packages (18 ounces each) Hawaiian sweet rolls
1-1/2 cups marinara sauce
24 slices fresh mozzarella cheese
1/2 cup butter, melted
Preheat oven to 350°. Place eggs and bread crumbs in separate shallow bowls. Dip eggplant slices in eggs; coat with crumbs. In a large skillet, cook eggplant in oil in batches until golden brown on both sides; drain on paper towels.
In a small bowl, mix ricotta, 1/3 cup Parmesan, lemon juice, 1 teaspoon parsley flakes, lemon zest and kosher salt. Spread over roll bottoms. Place in 2 greased 13x9-in. baking dishes. Top with eggplant, marinara and mozzarella. Replace roll tops. Brush with melted butter; sprinkle with remaining 1/4 cup Parmesan cheese and 1 teaspoon parsley.
Bake, uncovered, until golden brown and cheese is melted, 15-20 minutes. Serve with additional warmed marinara.