In a bowl combine all ingredients except cheese. Form mixture into 8 patties about -inch thick. Top 4 of the patties with cheese. Top them with the four remaining patties and seal in the edges. Cook patties over medium-high heat on a lightly-oiled grill for 4-5 minutes per side, or until cooked through. Serve patties in pita bread with tzatziki or yogurt, sliced cucumbers, sliced tomatoes, pitted olives and sprouts.
Recipe Options: Ground lamb, turkey, pork or chicken could be used instead beef. Soft goat cheese could be used instead of feta.