Set up grill for direct cooking over high heat. Oil grate when ready to start cooking.
In a food processor, combine walnuts, garbanzo beans, bread crumbs, grill seasoning, paprika, pepper flakes, oil and vinegar and pulse until coarsely ground.
In a small bowl whisk egg, add to food processor and pulse for 10 seconds, just enough to incorporate egg. Divide into 4 equal-size parts; roll into balls, and flatten with the palm of your hand into 3/4-inch-thick patties.
Place burgers on oiled grill. Cook 4 minutes per side.
Serve hot on toasted buns with lettuce, tomato, avocado and honey mustard.