Preheat an oven to 350 degrees F (175 degrees C). Grease a baking sheet.

Peel 2 of the eggplants and cut lengthwise into 1/4-inch-thick slices. Dice the remaining eggplant and any scraps; soak the diced eggplant in lightly-salted, cold water. Sprinkle the eggplant slices with salt and set aside as you prepare the remaining ingredients.

Pour 3/4 cup of seasoned breadcrumbs into a bowl; set aside. Stir together the flour, 1/2 teaspoon minced garlic, 1/2 teaspoon minced onion, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, and 1/2 teaspoon basil in a bowl; set aside. Beat the egg with 2 tablespoons of water in a separate bowl. Rinse the salt off of the eggplant slices and wipe off excess water. Coat the eggplant slices in the flour mixture, dip into the egg, and press into the bread crumbs. Place the eggplant slices onto the prepared baking sheet.

Bake in the preheated oven until the eggplant slices are golden brown and tender, about 10 minutes. Turn once as they cook to brown both sides; set aside and allow to cool until you can easily handle.

Meanwhile, heat the olive oil in a large skillet over medium heat. Stir in 1 chopped onion and 1 1/2 tablespoons minced garlic; cook and stir until the onion is soft and translucent, about 5 minutes. Add the whole jumbo shrimp and cook until pink and no longer translucent in the center, about 5 minutes. Remove the shrimp and set aside. Stir the diced shrimp into the skillet and cook until no longer translucent. Season with 1 pinch garlic powder, 1 pinch onion powder, 1 teaspoon basil, red pepper flakes, and the white wine. Drain the water from the diced eggplant and squeeze out the excess water. Stir the eggplant into the shrimp mixture and bring to a boil. Reduce heat to medium, cover, and cook until the eggplant is soft, about 10 minutes; stir in the mozzarella cheese and 1/2 cup of bread crumbs until the cheese has melted.

To assemble, place one jumbo shrimp onto the center of each eggplant slice. Spoon about 2 tablespoons of the stuffing over each jumbo shrimp. Fold the ends of the eggplant over the stuffing and secure with toothpicks. Place the eggplant rolls onto the baking sheet.

Bake in the preheated oven until the eggplant rolls are hot in the center, about 5 minutes. Remove the toothpicks before serving.