In a small bowl, mix the ground flaxseeds and water, or egg, Worcestershire or miso, and vinegar and let sit at room temperature for 15 minutes.
In a food processor fitted with the metal blade, combine the walnuts, garlic powder, cumin, coriander, salt, and pepper and process until fine and crumbly, 30 to 90 seconds. Add the flax mixture, mushrooms, and oats. Pulse (do not puree) until a coarse mixture forms, about 1 minute more.
In a large bowl, dump the beans and quickly smash with a potato masher just until the mixture is coarse and lumpy with some whole beans. Add the walnut mixture and stir to combine.
Measure 1/2 cup of the bean mixture and form into a patty, then place on a plate. Repeat the procedure with the remaining bean mixture. The patties can be cooked immediately or refrigerated overnight, if you wish.
In a large skillet or griddle over medium-high heat, warm 2 tablespoons oil. Working in batches, if necessary, cook the patties until heated through and browned on the outside, 3 to 5 minutes per side. Repeat with remaining patties, adding more oil as needed.