Preheat the oven to 400°F. Line a sheet tray with a wire rack and set aside.
In a large bowl, combine ground meat, dill, half of the parsley, 2 tablespoons of olive oil, the juice of 1 lemon, 1 teaspoon cumin, 1 teaspoon coriander, and chili flakes. Work together with your hands until well combined.
Using a sharp knife, score the pita in half, then cut it in half to create a pocket. Stuff each pita pocket with the meat mixture, pressing gently to pack and microwave for 15 seconds to soften. Divide the meat filling into a portion, then spread each pita pocket with the meat mixture, pressing gently to pack and microwave for 15 seconds to soften.
Heat a thin layer of olive oil in a large skillet over medium heat. Working in batches, cook the stuffed pita in the hot oil for 2-3 minutes per side, until golden brown. Transfer to the prepared sheet tray and bake in the oven for 5-10 minutes, or until warmed and golden brown. Finish with the yogurt side.
Transfer the cooked pita to a wire rack lined sheet tray. Bake for 10-15 minutes, or until the meat reaches an internal temperature of 165°F.
In a small bowl, combine the cucumber, radish, feta, 2 tablespoons olive oil, the juice from the remaining lemon, remaining parsley, and remaining cumin. Toss well with salt and pepper to taste.
Serve the arayes on a bed of salad on a large platter and drizzle by the yogurt on top. Serve with dollops of Greek yogurt and a drizzle of olive oil. Finish with freshly ground black pepper.