Make shichimi aioli: In a small bowl, whisk mayonnaise with shichimi togarashi until smooth.
Preheat grill or grill pan to high. Form beef into 4 equal patties and brush patties with teriyaki sauce. Grill to desired doneness, about 4 minutes per side for medium, adding cheese during the last minute of cooking.
Split Kings Hawaiian’s Original Hawaiian Sweet Hamburger Buns, then toast on grill. Grill pineapple slices until charred.
To assemble burgers, spread aioli on bottom buns, then top with burgers, onion, tomato, pineapple, lettuce, and pickles.