Heat the oven to 425°F.

Place the following in a food processor in the following order: ½ chopped small red onion, 6 fresh parsley sprigs, 3 coarsely chopped garlic cloves, 2 teaspoons kosher salt, 2 teaspoons dried oregano, 1 teaspoon ground coriander, and ½ teaspoon black pepper, 8 ounces lean ground beef, and 8 ounces ground lamb. Process until the mixture forms a sticky paste, scraping down the sides of the food processor as needed, about 1 minute total.

Arrange a large sheet of parchment paper (roughly 13 by 16 inches) on a work space with the short edge closer to you. Scrape the meat mixture onto the parchment. Use wet hands to press it into a large flat rectangle about ½-inch thick.

Cover with a second large sheet of parchment paper. Use a rolling pin to roll the meat mixture into an even layer about ¼-inch thick (the meat will extend to the edges of the parchment). Starting from the short end closest to you, roll the meat, still encased in both sheets of parchment, into a roll that’s about 2 inches wide. Place the roll seam-side down on a rimmed baking sheet.

Bake until the meat is browned and cooked through, 20 to 25 minutes. Meanwhile, make the sauce.

Stir 1 cup plain Greek yogurt, 1 teaspoon lemon juice, ½ teaspoon dried dill, and ¼ teaspoon garlic powder together in a small bowl. Taste and season with kosher salt and black pepper as needed.

Let the meat cool for about 5 minutes. Unroll and discard both sheets of parchment paper. Cut the meat crosswise into rough 1-inch-wide strips. Divide the meat between 4 warm pita breads and top with a generous amount of sauce and toppings as desired.