Garlic and spices give the meat big flavor without tons of added fat and salt.
Place a rack in center of oven; preheat to 400°F. Rub carrots with 1/2 Tbsp. oil; season with 1 tsp. cumin, salt and pepper. Arrange in a single layer on a rack in a roasting pan. Whisk together remaining 1 1/2 Tbsp. oil, vinegar, chili powder, garlic, remaining 1 tsp. cumin, 1 tsp. salt, and 1/2 tsp. pepper in a small bowl. Rub chicken all over with spice mixture; place onion and lemon wedges in cavity. Tie legs with kitchen string and place onion on top of carrots on rack. Add 1 cup broth to bottom of pan.
Roast chicken, adding more broth to pan as needed, until carrots are tender, chicken is golden brown, and an instant read thermometer inserted into center of a thigh reads 165°F, 1 1/4 to 1 1/2 hours.
Let chicken rest for 10 minutes before carving. Squeeze half of lemon wedges into pan juices; discard wedges and onion. Transfer carrots to a serving dish. Skim fat from pan juices. Carve chicken and serve with carrots, pan juices, and fresh lemon wedges.