For the donkey sauce: Mix together the mayonnaise, roasted garlic, mustard, salt, Worcestershire, black pepper and lemon juice in a small bowl. Refrigerate until ready to use.
For the wet soak: In a nonreactive bowl or gallon resealable bag, combine the buttermilk, hot sauce, basil, granulated garlic, white pepper and beaten egg and mix well. Add the oysters (or shrimp) and any liquid from shucking. Cover and refrigerate 15 minutes.
For the breading and frying: In a shallow bowl, combine the panko, cornmeal, flour, dried basil, granulated garlic, 1 teaspoon of the sea salt, the black pepper, cayenne and paprika and mix well.
Heat the oil in a large cast-iron skillet until a deep-frying thermometer inserted in the oil registers 350 degrees F.
Drain the oysters (or shrimp) from the wet soak and dredge through the breading mixture, pressing gently to adhere. Carefully add to the hot oil in batches (do not crowd) and cook 3 to 4 minutes per side. Remove to a paper-towel-lined plate and season with the remaining 1 to 2 teaspoons sea salt while hot.
For the sandwiches: Preheat the oven to a low broil. Butter the rolls with the garlic butter and place on a baking sheet. Broil until golden, 2 to 3 minutes.
Spread Donkey Sauce on both halves of each roll. Layer on the oysters, cabbage, pickles and tomatoes and top with the other half of each roll. Serve immediately.