Using a vegetable peeler peel the carrot and cucumber into long ribbons. Combine the rest of pickles ingredients, add the vegetables, and let sit at room temperature while preparing the burgers and sauce.
Make the burgers:
Pulse the nuts in a food processor until finely ground. Transfer to a mixing bowl. Pulse the beans until coarsely chopped. Add to the almonds along with the breadcrumbs, onion and garlic powders, salt, pepper, 2 tablespoons ponzu sauce, and 3 tablespoons of the reserved bean liquid. Mix well. Shape into 4 equal sized patties and refrigerate for at least 30 minutes.
Heat a skillet over medium-high heat. Add the oil and let it get hot. Brush the remaining tablespoon of ponzu sauce on one side of the burgers. Place sauce side down in the skillet. Cook for 2-3 minutes per side.
Serve on buns with sauce and quick pickles.
Make the sauce:
Combine all sauce ingredients mixing well. Cover and refrigerate until serving time.