Whisk the mayonnaise, sesame oil, and seasoned rice vinegar together in bowl. Cover and refrigerate until ready to serve. Mix the panko, egg, soy sauce, mustard, and garlic powder together in a medium bowl. Add the pork, sugar, salt, and the ground black pepper. Mix until evenly combined. Gently form the mixture into 16 golf ball-sized balls, then press each ball into a 1/2-inch thick patty. Heat a large skillet over medium-high heat and add about half of the oil. Cook the patties, in batches, until cooked through and golden brown, about 3 minutes a side. Tuck the patties into the rolls and top with the reserved sesame mayonnaise and lettuce. Serve.
Serve with the White Russian.