In a large skillet, combine the sugar, mirin, soy sauce, and wine/sake over medium heat. Stir for 3-5 minutes until the mixture bubbles and the sugar dissolves, then pour the sauce into a dish to reserve and drizzle the olive oil in the pan.

Meanwhile, combine the beef, Sriracha, and Worcestershire sauce in a large bowl. Form into 16 even patties, about ½ inch thick, slightly larger in diameter than the slider buns.

To the teriyaki sauce skillet with the oil, add the sliders a few at a time (you may need to cook a few batches) and increase the heat to medium-high. Cook for 2-4 minutes, then flip when the burgers are golden on the first side. Once you flip the burgers, add enough teriyaki sauce to the pan to evenly coat the bottom of the pan in a thin layer. Cook the burgers for 2 minutes on the second side, then flip around in the sauce to coat.

Serve on slider buns topped with lettuce with extra teriyaki sauce or Sriracha, if you'd like.