Put the ground beef in a bowl on the counter and allow the chill to come off, about 5 minutes.
Combine the teriyaki sauce, chicken broth and brown sugar in a saucepan over medium-high heat and reduce by half, stirring occasionally, about 10 minutes. Add the pinch of cayenne, remove from heat, and cool to room temperature.
Reserving half of the sauce, combine the other half with the meat, garlic and onions. Mix well but do not squeeze, mash or overmix. Being gentle, shape into four even patties.
Either broil or cook over the grill, roughly 6 minutes on each side for medium, mopping with the remaining marinade. Let burgers rest for a few minutes before serving on toasted rolls with your favorite toppings!