Whisk the soy sauce, water, brown sugar, rice vinegar, ginger, garlic and cornstarch in a small saucepan.
Simmer the teriyaki sauce for 2 to 3 minutes until glossy and thick enough to coat a spoon.
Mix the turkey with the panko, egg and salt gently and shape 4 patties with damp hands.
Cook the patties in a lightly oiled skillet over medium heat for 6 to 7 minutes per side until the centers reach 165°F.
Move the patties off the heat and brush each with 1 tablespoon teriyaki sauce.
Sear the pineapple rings in the same skillet for 1 to 2 minutes per side until browned at the edges, then toast the buns.
Build each burger with cabbage, one glazed turkey patty, one pineapple ring and another spoonful of teriyaki sauce.