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°. 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. Place carrots in the bowl and toss to coat.
Spread the carrots out evenly in a single layer on a baking sheet. Transfer carrots to the hot oven and roast carrots for between 15 and 20 minutes or until they begin to turn golden brown. After 10 minutes of roasting, add the foil-wrapped pitas to separate oven rack. Heat for the remainder of the roasting time, about 10 minutes. Remove all from the oven and set aside to cool.
Melt butter in a shallow saucepan over medium-low heat and brown. NOTE see my instructions for browning butter in the notes below. Add raisins, sliced almonds, 1/2 teaspoon thyme, and remaining the 1/2 teaspoon of sumac. Cook gently until the raisins puff up, about 1 minute. Let cool.
To the now room temperature yogurt, add 1/4 teaspoon salt, and remaining 1/2 teaspoon thyme and whisk. Spread yogurt onto a pretty serving platter. Toss the carrots with the raisin-nut mixture and the chopped parsley. Spoon over yogurt and serve drizzle with olive oil and finish with a liberal pinch of sea salt if desired. Unwrap the warmed pitas and serve alongside the carrot platter.