Mix the meat, yogurt, herbs, egg, and seasonings in a large bowl.
Mix together the ingredients until well combined and place in the refrigerator for at least 30 minutes for the flavours to combine
Preheat the grill to medium-high heat
Remove the meat from the refrigerator and shape it into 8 large flat patties.
Place about 2 ounces of the Greek feta cheese onto one of the patties and, place a second patty directly over the cheese and seal the two patties together by pressing the edges closed, sealing in the cheese, continue to stuff the patties with feta until all the bifteki’s are prepared.
Cook the bifteki for about 3 to 4 minutes per side on the preheated grill or lightly oil a griddle and cook the bifteki for about 5 minutes per side.
Place the bifteki’s on a lightly grilled piece of pita bread and garnish with fresh lettuce, cucumbers, tomatoes, onions, and tzatziki sauce and enjoy!