Preheat the oven to 400°F.
In a large bowl, combine the ground beef, onion, garlic, sumac, smoked paprika, cumin, dill, green chili flakes, and Greek yogurt. Mix thoroughly until the seasonings are evenly distributed throughout the meat.
Lay a long sheet of parchment paper onto a clean work surface. Place the meat mixture in the center and press it into a rough rectangle. Top with a second sheet of parchment paper and use a rolling pin or your hands to flatten the meat into a very thin, even layer.
Remove the top sheet of parchment. Starting from the short end, tightly roll the parchment and meat together into a spiral-shaped log, allowing the parchment to separate each layer of meat as you roll.
Transfer the roll to a baking sheet and bake for 20–25 minutes, or until the center reaches 160°F and the meat is fully cooked through.
Let the roll rest for 10 minutes before carefully unrolling it. The meat should naturally separate into thin strips as it opens. Allow it to cool another few minutes so the juices can settle, then tear any larger pieces into bite-sized strips.
Serve the doner meat inside toasted pita bread with lettuce, cucumber, tomatoes, onion, chilis, and a spoonful of Greek yogurt. Enjoy!