For the sauce: Combine the cornstarch in cold water and dissolve. Set aside to thicken.
In a small saucepan, mix soy sauce, pineapple juice, brown sugar, grated ginger and garlic over medium heat. Bring to a boil and simmer until sauce reduces, about 15 to 20 minutes.
Add cornstarch and water mixture, simmer until thick, about 5 minutes. Remove from heat and set aside to cool.
For the burgers: Combine the ground beef with grated carrots, scallions, jalapeno pepper, ginger, soy sauce and sriracha sauce. Mix throughout but don't overwork the mixture so the patties don't get tough. Form 8 equal sized patties.
On the grill: Place the patties on the hot grill and cook until they reach desired doneness, grilling the pineapple next to the patties during the last 5 minutes or so. Optionally, you could brush a little teriyaki sauce on the pineapple slices as they grill.
To serve, place a piece of lettuce on the bottom of each burger bun. Top with the cooked burger and 1 tablespoon (or more) of teriyaki sauce, top with grilled pineapple and any other fixings you want to include.