Heat your grill to a medium-high temperature. If using the Big Green Egg, you’ll want the temperature to get to about 500 degrees Fahrenheit.
First, make the teriyaki sauce. Combine all ingredients except cornstarch in a small saucepan over medium-low heat. Let come to a low simmer, then whisk in cornstarch until sauce begins to thicken. Turn off heat and let sit at room temperature while you make the burgers.
In a medium mixing bowl, combine all burger ingredients. In this situation, it’s probably easiest to just get in there and mix everything together with your hands.
Once burger ingredients are combined, use your hands to form slider-size patties (make a ball about the size of a lacrosse ball, then flatten it slightly and use your thumb to place an indent in the center to allow the meat to expand while cooking.)
Place sliders on the prepared grill and cook for just a few minutes each side. Since the patties are small, they won’t take much time at all to cook.
Remove burgers from the grill and immediately brush with some of the prepared teriyaki sauce. Reserve the remaining sauce to serve as a condiment.
Serve burger patties alongside sliced Hawaiian rolls and the rest of the suggested condiments. Let guests build their sliders as they please!