Preheat oven to 400 degrees. Peel carrots. On a baking sheet toss carrots with olive oil. Add spices and toss. Place in oven and cook for 30 minutes, flipping at 15 minutes.
Meanwhile slice chicken breasts into 1/2 inch bite sized pieces. On a separate baking sheet, place chicken. Squeeze juice over chicken. Add spices and toss until evenly distributed. Place chicken in oven and bake till chicken is cooked though, about 23 minutes. Once done, set aside and let rest.
As the chicken and carrots are cooking, prepare rice. Add olive oil to a medium pot on medium high heat. Add onion and garlic, stirring so garlic does not burn, and cook about 2 minutes. Add spices and stir to distribute evenly. Add rice, chicken broth an lemon juice. Bring to a boil and then cover and reduce to a simmer till rice is thoroughly cooked through, about 20 minutes.
Make Taziki: Stir together yogurt with dill, garlic powder and pepper. Place in refrigerator till ready to serve.
Serve: Place rice on bottom, then chicken. Add dollops of hummus and taziki on top of chicken.Sprinkle parsley and tomatoes on top. Scoop up with pita chips, naan or pita bread.