In a small saucepan combine soy sauce and sugar. Bring to a boil, stirring constantly, until the sugar is dissolved. Whisk in cornstarch mixture, allow it to return to a boil just until thickened, then take off the heat.
In a large bowl mix beef, 1 teaspoon salt, and pepper with your hands just until well-combined. Use a ⅓ cup measure to portion beef mixture, shaping each portion into a small patty.
Heat a large nonstick skillet over medium heat. Add beef patties in batches and cook, flipping once, until browned on both sides and cooked to desired degree of doneness, 2-3 minutes per side. Just as the burgers finish cooking, brush them lightly with teriyaki glaze. Transfer to a large plate or baking sheet. Repeat cooking and glazing with remaining patties.
Wipe out the skillet and place back over medium heat. Add pineapple rings and brush lightly with teriyaki glaze. Cook until lightly browned on the bottom, then flip, brush with more glaze, and continue cooking until pineapple is caramelized. Transfer to a cutting board and cut pineapple into wedges.
In a medium bowl, mash avocado with remaining 1 teaspoon salt and lime juice.
Lay slider bun bottoms on a countertop and top each with a butter lettuce leaf, a burger, a spoonful of mashed avocado, and a few pineapple pieces. Cover with the tops of the buns and serve immediately.