Split the beef into 4 pieces and shape into patties that are a bit larger than the buns as they will shrink as they cook. Salt and pepper the patties. If your ground beef is very lean (less than 10% fat), then you'll want to drizzle a little olive oil onto the patties.

Put the onions in a tray or bowl and drizzle with olive oil, flipping a few times to coat evenly. If you have skewers, pass a skewer through the center of each slice of onions to keep the rings from separating on the grill.

Peel the pineapple, and then cut into ⅓-inch thick slices. Use a small cookie cutter or paring knife to remove the core. Drizzle with olive oil.

To make the teriyaki sauce, add the sugar, pineapple juice, and soy sauce to a small saucepan and boil until the mixture has reduced to about 30% of its original volume and it's about the thickness of maple syrup (the real stuff). Remove from the pan from the heat and set aside.

Put the hamburger patties on the grill along with the pineapple and onions. Let them all get grill marks on one side and then flip over. Use an instant read thermometer to tell when the burgers are done. When the burgers are almost done, split the buns, and toast them on the grill.

To assemble, put the grilled pineapple on the bottom bun, followed by the burger patty, tomato and grilled onions. Drizzle a generous amount of teriyaki sauce onto your island burger and top with with the top bun.