Pulse the walnuts in a food processor until finely ground. Transfer to a mixing bowl. Pulse the black beans until coarsely chopped. Add to the walnuts along with the breadcrumbs, onion and garlic powders, salt, pepper, 2 tablespoons teriyaki sauce, and 3 tablespoons of the reserved bean liquid. Mix well. Shape into 4 equal sized patties and refrigerate for at least 30 minutes.
While the burgers are chilling, make the accompaniments. Heat a skillet or grill pan over medium-high heat. Cook the pineapple rings for 2-3 minutes per side. Cook the onion slices until browned and softened, about 5 minutes.
Puree the roasted red pepper in a food processor. Stir into the mayonnaise, adding some Sriracha, if desired.
Heat a skillet over medium-high heat. Add the oil and let it get hot. Brush the remaining tablespoon of teriyaki sauce on one side of the burgers. Place sauce side down in the skillet. Cook for 2-3 minutes per side.
To assemble, spread each side of the buns with the mayonnaise. Top with the burgers, pineapple, onion, and some cilantro.