For a refreshing sauce, combine 1/2 cup Greek-style yogurt, 3 tablespoons minced cucumber, 1 teaspoon fresh chopped dill, and a pinch of salt.
Combine first 11 ingredients in a bowl, and form mixture into 4 large patties about 1/2 inch thick. (Patties will be soft.)
Heat oil in a nonstick skillet over medium heat. Add patties, and cook 5 minutes on each side. Serve on buns; garnish, if desired.