In a medium saucepan, cook rice in water, covered, about 45 minutes or until soft and sticky. Measure 2 cups rice.
Meanwhile, in a food processor bowl, process navy beans until mashed. (Or place beans in a large bowl and mash with a potato masher.) Combine beans, peanuts, sunflower seeds, and walnuts or pecans. Set aside.
In a large skillet, cook celery, carrot, onion, and garlic in the 1 tablespoon cooking oil until the vegetables are tender. Add to the nut mixture. Add beaten egg whites, soy sauce, tomato paste, oregano, sage, basil, pepper, and cooked rice. Mix well.
Form into ten 3/4-inch-thick patties. In a large skillet, heat 1 to 2 tablespoons cooking oil over medium heat. Cook 4 to 5 patties at a time about 3 minutes per side or until browned and heated through. Repeat with remaining oil and patties. Serve in buns as you like, with desired toppers. Makes 10 burgers.