Spoon the yogurt into a bowl. Set aside and allow it to come to room temperature while you prepare the carrots and the pitas.
Preheat oven to 450°F. In a medium bowl, combine 3 tablespoons of the olive oil, 1/4 teaspoon of the Kosher salt, and 1 teaspoon of the sumac.
Use a pastry brush to brush the sumac oil all over each pita. Stack the breads after oiling and cut in halve. Wrap the stack in heavy gauge aluminum foil and set aside.
Wash and trim the carrot tops to 1-inch. Set tops aside for another use. Use a sharp kitchen knife and CAREFULLY run the knife right down the middles to create halves.
Using the same bowl used for the sumac oil, add an additional 1 teaspoon sumac and 1/2 teaspoon Kosher salt followed by fresh lemon zest, coriander, cumin, and remaining 2 tablespoons of olive oil.