Preheat the oven to 425°F. Prepare a half sheet pan with a wire rack. Add the 1 tablespoon of sumac, salt, black pepper, coriander, cardamom, and cinnamon to a small bowl. Mix to combine.
Place the chicken thighs onto the rack and drizzle both sides with olive oil. Rub to coat. Sprinkle the spice mixture onto each side of the chicken, lightly pressing it in. Roast the chicken skin-side up for 35-40 minutes, or until crisp and cooked through.
Place the carrots onto another half sheet pan. Drizzle with olive oil and toss to coat. Arrange the carrots into an even layer. Season with salt and black pepper. Roast for 25 minutes.
Remove the pan from the oven and drizzle the pomegranate molasses over the carrots. Use a spatula to gently toss. Arrange the carrots back into an even layer. Sprinkle the sesame seeds over top. Roast for another 5 minutes, or until the carrots are caramelized and tender.
Meanwhile, add the yogurt, tahini, lime zest, lime juice, garlic, 2 tablespoons of olive oil, and the remaining 1 teaspoon of sumac to a mixing bowl. Whisk to combine. Season with salt to taste.
Serve the chicken with the carrots and yogurt alongside. Top with pomegranate seeds, fresh dill leaves, and an extra sprinkle of sesame seeds.