Preheat oven to 375 degrees.
Cut zucchini in half lengthwise and then in 1/2 inch slices. Cut carrots into 1/4 inch rounds. In a large bowl, toss carrots and zucchini with 2 Tbsp. olive oil, 1/2 tsp. cumin, 1/4 tsp. paprika and 1/2 tsp. salt. Then, transfer to a high-top baking pan. Pat chicken dry and season with salt and pepper on both sides. Heat 1 Tbsp. olive oil in a large skillet over a medium heat. Add the chicken breasts, skin side down. Cook 2-3 minutes until skin is golden brown. Remove chicken breasts and transfer, skin side up, to the pan with zucchini and carrots. Place in the oven and roast for 30 minutes, or until the internal temperature reaches 165 degrees. Remove from oven; divide chicken and roasted veggies between two plates and garnish with minced dill.