In a small saucepan, bring water to a boil. Add quinoa. Reduce heat; simmer, covered, until liquid is absorbed, 12-15 minutes. Remove from heat; fluff with a fork., Meanwhile, place carrot in a food processor; pulse until coarsely chopped. Add beans; process until chopped. Transfer mixture to a large bowl. Mix in cooked quinoa, bread crumbs, green onions, egg and seasonings. Shape mixture into 8 patties., In a large skillet, heat oil over medium heat. Add patties; cook until a thermometer reads 160°, 3-4 minutes on each side, turning carefully. If desired, serve with optional ingredients.