Remove and discard stems and discolored spots from greens. Wash greens thoroughly; drain and cut into 1/2-inch strips. Set aside.
Cook fatback and hog jowl in hot oil in a 6-quart Dutch oven over medium heat, stirring often, 8 to 10 minutes or until fatback is crisp. Remove fatback and jowl, and set aside. Drain, reserving 1/4 cup drippings.
Bring 4 cups water, next 3 ingredients, and 1/4 cup reserved drippings to a boil in Dutch oven over medium-high heat. Add one-third of greens, stirring often, 2 to 3 minutes or until wilted. Repeat procedure twice with remaining greens. Reduce heat to low; cover and cook, stirring occasionally, 45 minutes or until collards are tender. Add additional sugar and salt to taste, if desired.