Add the ground beef, island teriyaki, and bread crumbs to a large mixing bowl. Mix everything together until well combined. Cover the bowl with plastic wrap and chill for 1 hour.
Preheat the grill to medium-high heat.
Take the ground beef out of the fridge and for the mixture into 4 evenly sized patties. Set aside. Cut the cored bell pepper into 4 large pieces. Set aside.
Grill the burgers for 3-4 minutes per side (for medium) or until cooked to your desired doneness. Remove from the grill to a plate.
Grill the pineapple rings for 2-3 minutes per side and the bell pepper pieces for 4-5 minutes per side. Remove from the grill to a plate. Toast the bun side of the burger buns for 1-2 minutes on the grill.
Place one burger patty on the bottom hamburger bun. Top with a pineapple ring and a bell pepper piece. If desired, you can drizzle a little extra teriyaki sauce over the bell pepper. Put the top bun in place and serve immediately.
Notes
You can use a grill pan on an indoor stovetop if you don't have an outdoor charcoal or propane grill.