In a small bowl, combine the ingredients for the tzatziki sauce. Cover and place in the fridge for a 1 hour to allow flavors to meld (optional).
To make the burger patties, mix the ground turkey, oregano, garlic, onion, parsley, cumin, pepper and salt in a bowl with your hands until fully combined. Divide the mixture into 6 evenly sized burger patties, slightly larger than the hamburger buns.
Heat the oil in a large cast iron skillet set over medium heat**. Season the outside of the patties with a little sprinkle of salt. Cook the patty for 4-5 minutes on each side. Use a food thermometer to be sure they have reached a safe minimum internal temperature of 165 °F.
To assemble the burgers, layer them with tzatziki sauce, the patty, tomato, lettuce more tzatziki sauce and feta. Enjoy.