Bring water to a boil in a small pot over medium high heat. Add bulgur, cover, reduce heat to medium low and simmer until water is almost absorbed and bulgur is just tender, about 10 minutes. Remove pot from heat and set aside for 5 minutes. Uncover pot, fluff bulgur with a fork and set aside until cooled.
Grease grill grates with oil and preheat to medium heat. Meanwhile, in a large bowl, mix together beef, bulgur, parsley, cumin, cinnamon, allspice and chopped onion. Form mixture into 6 patties and season all over with salt and pepper.
Grill patties, flipping once, until deep golden brown and cooked through, 5 to 7 minutes per side. (Alternatively, cook burgers using 1 Tbsp. canola oil in a large skillet over medium heat.) Transfer burgers as done to hamburger buns, top with lettuce, tomatoes and sliced onions and serve.