Preheat oven to 425°F (220°C).
In a large bowl, combine the beef, lamb, onion, garlic, yogurt, and all seasonings. Mix for 3–4 minutes until the mixture becomes smooth and paste-like.
Divide into 4 portions. Place each portion between sheets of parchment paper, flatten, then roll into a log shape.
Arrange on a sheet pan and bake for 15–18 minutes, until cooked through.
While the meat cooks, prepare the salad and tzatziki by mixing all ingredients in separate bowls.
Let the meat cool slightly, then slice into thin strips. Spread onto a sheet pan and broil for 3–5 minutes until browned and crispy.
Serve in warm pita or naan with salad, tzatziki, and feta if desired.
