How to Make It
Whisk together eggs and milk in a medium bowl. Stir together panko, 3/4 cup Parmigiano-Reggiano, and 1 1/4 teaspoons salt in a shallow dish. Set aside.
Pour oil into a large Dutch oven to a depth of 2 inches; heat over medium to 375°F. Butterfly shrimp by making a deep slit down back of each from head end to tail, cutting to but not through inside curve of shrimp. Devein shrimp. Dredge shrimp in panko mixture, shaking off excess. Dip in egg mixture, and dredge again in panko mixture, pressing to adhere.
Fry half of coated shrimp in hot oil until golden and crisp, about 1 minute and 30 seconds. Using a slotted spoon, transfer fried shrimp to a baking sheet lined with paper towels. Repeat with remaining shrimp, returning oil temperature to 375°F over medium-high before adding the second batch. Sprinkle fried shrimp evenly with remaining 1/4 teaspoon salt.
Preheat broiler to high with oven rack 6 inches from heat. Divide marinara among 4 shallow, broiler-safe, 8-ounce gratin dishes. Top evenly with fried shrimp and mozzarella. Place on a rimmed baking sheet, and broil until cheese is melted, 2 to 3 minutes. Sprinkle with remaining 1/4 cup Parmigiano-Reggiano. Top evenly with basil, and serve with garlic bread.