Stir together the bulgur and 1/2 cup boiling water in a small bowl; let stand 30 minutes or until water is absorbed and bulgur is tender.
Meanwhile, in a nonstick skillet, heat the olive oil over medium heat. Add the onion and sugar; saute until the onion is lightly browned, about 10 minutes. Stir in the vinegar; saute about 20 seconds, stirring until vinegar evaporates. Remove the skillet from the heat.
In a small bowl, mix the plumped bulgur, onion mixture, beef, carrot, garlic, Worcestershire sauce, salt and pepper.
Shape into 3/4-thick patties.
Grill or broil the burger patties on a rack sprayed with vegetable cooking spray until browned and cooked, about 5 minutes per side.