Add all ingredients for the Hawaiian teriyaki sauce in a small saucepan over medium-low heat. Stir frequently until the sugar has dissolved. Remove from heat and set aside to cool. Store in an airtight container for 2 weeks.
Heat a grill or grill pan over medium-high heat. Spray with a nonstick spray, and add the burgers. Cook for about 4 minutes on each side for medium-rare. Melt the cheese on the burgers for the last two minutes of cooking time. Remove from heat and set aside to rest.
Assemble your burgers by layering the burger patties, lettuce, pineapple, bacon and avocado on the toasted buns. Drizzle with Hawaiian teriyaki sauce and sprinkle with sesame seeds.