SWEET TERIYAKI SAUCE: Combine cornstarch and cold water. Stir with a fork until dissolved and set aside. Mix soy sauce, pineapple juice, brown sugar, and grated ginger in a small saucepan over medium-low heat. Bring to a boil and then lower the heat and simmer until the sauce reduces, about 15 to 18 minutes. Whisk together the cornstarch-water mixture again and pour into the pan. Stir and continue to simmer until sauce thickens, another 2-3 minutes. Remove from heat and set aside to cool.
PREHEAT THE GRILL: Heat the grill to 450 to 475 degrees F.
BURGERS: In a large mixing bowl, add the (cold straight from the fridge) beef, garlic, ginger, and soy sauce. Mix the meat just a few times (no longer than for 30-40 seconds) until ingredients are incorporated. Be careful to not overwork or overhandle the meat.
SHAPE: Line a large sheet pan with two layers of parchment paper. Shape the burger patties on the tray instead of with your hands (this helps keep them from being over handled while also providing leverage to get the patties firm). Divide the meat into 3 equal parts. Gently form each portion into a patty that is about 4 to 4 and 1/2 inches across and with 1-inch sides. Make a shallow depression in the middle (see pictures in the post). The depression keeps the patty from shrinking too or puffing up too much. Cover with plastic wrap and refrigerate until the grill is completely heated.
GRILL BURGERS: Prepare the preheated grill by cleaning with a grill brush. Generously oil the grill (I drench a roll-up paper towel in vegetable oil and, holding it with tongs, rub it over the grill grates). Remove burgers from the fridge and generously salt and pepper both sides of the patties. Hold your hand 6-7 inches above the meat and sprinkle the seasoning liberally or to taste. In total, I use about 1 and 1/2 teaspoons each of salt and pepper to all the patties. In a small bowl, combine 2 tablespoons pineapple juice and 2 tablespoons of the sweet teriyaki sauce. We will baste this over the burgers.
PINEAPPLE: Drizzle vegetable oil over the pineapple (this helps keep it from sticking). Place pineapple slices on the heated grill and cook, flipping once, until tender, golden, and lightly charred-- about 2-4 minutes per side. Remove and set aside. OPTIONAL: Grill red onions by drizzling with vegetable oil and cooking for 1-3 minutes per side or until crisp-tender and lightly charred.
BURGER TEMPERATURES: Place patties INDENTED SIDE DOWN on the grill. Cook to desired doneness: Rare burgers: 125 degrees F (about 4 minutes total) Medium-rare burgers: 135 degrees F (about 5 minutes total) Medium burgers: 145 degrees F (about 6-7 minutes total) Well-done burgers: 160 degrees F (about 8 minutes total) (We like medium-rare best) Flip the burgers once during cooking, at the halfway mark. Never press down on the patties (this will make fat and flavor escape. Use a wide metal spatula for best results. Baste the burgers with the prepared sauce occasionally as you grill.
CHEESE: In the last minute of cooking time, add a slice of Swiss cheese to each patty. Remove patties to a plate and cover with foil to rest for 1-2 minutes.
GRILL BUNS: Melt 2 tablespoons butter and then brush (with a pastry brush) over both sides of all the buns. Set aside. When you have about 1 minute left on the cooking time for the patties, add the buttered buns to the grill (over indirect heat, alongside the edges of the grill). Watch carefully; they toast in about 30 seconds to 1 minute.
SERVE: Assemble by adding mayo to buns and topping with lettuce, cheese-covered burger patty, grilled pineapple, a spoonful (or 2 -- to personal preference) of the sweet teriyaki sauce, grilled red onions, tomatoes, and the top of the bun. Enjoy immediately.