Combine first 4 ingredients; shape into 6 patties.
Cook patties in a large nonstick skillet, in batches, over medium-high heat 3 minutes on each side. Remove patties from skillet.
Add onion and 1/4 cup water to skillet; cook, covered, over medium heat 15 minutes. Uncover and stir; cook 10 more minutes. Remove half of onion from skillet. Return patties to skillet. Top patties with reserved onion; cover, reduce heat, and simmer 10 minutes.