Butterfly the shrimp by slicing along the backs and cutting about halfway into the flesh. Whisk the eggs, milk, paprika and 1 teaspoon salt in a shallow bowl; add the shrimp and refrigerate at least 15 minutes and up to 1 hour.
Put the flour in a shallow bowl and season with pepper. Put the breadcrumbs in another shallow bowl. Remove the shrimp from the egg mixture and dredge in the seasoned flour. Dip the shrimp in the egg mixture again, then roll in the breadcrumbs to coat; transfer to a rack set over a baking sheet and refrigerate until ready to fry.
Combine the mayonnaise, pickle, ketchup, horseradish, Worcestershire sauce, scallions and parsley in a small bowl. Cover and refrigerate until ready to serve.
Heat about 1/2 inch peanut oil in a large skillet over medium-high heat until a deep-fry thermometer registers 350 degrees F. Working in batches, add the shrimp and fry, flipping halfway through, until golden brown, about 5 minutes. Remove the shrimp with a slotted spoon and drain on paper towels; season with salt.
Spread the mayonnaise mixture on the rolls and fill with shredded lettuce and the fried shrimp. Serve with lemon wedges.