A tingly spice rub made of coriander, cumin, and mustard seeds infuses chicken with flavor, making the usual breading dispensable.
Preheat oven to 325 degrees. Toast coriander seeds, cumin seeds, and mustard seeds in a small dry skillet over medium heat, tossing occasionally, until fragrant, 4 to 5 minutes. Transfer to a plate to cool. Grind to a fine powder in a spice grinder or with a mortar and pestle. Transfer to a bowl; stir in nutmeg and cayenne with a fork. Add chopped cilantro, scallions, salt, and ginger; stir to combine.
Place carrots and onion in a 13-by-9-inch baking dish. Stir together coconut milk, carrot juice, and ginger in a glass measuring cup. Pour 1 cup mixture over vegetables, and transfer to oven; cook 12 minutes. Remove from oven.
Dredge chicken in spice mixture to coat. Set on top of vegetables; drizzle with remaining coconut-milk mixture. Cook until chicken is cooked through, 25 to 30 minutes. Transfer chicken and vegetables to a plate, and tent with foil.
Ladle about 1 1/2 cups pan juices into a small saucepan. Bring to a simmer; cook until reduced by half, 6 to 7 minutes.
Divide chicken and vegetables among 4 plates; drizzle with sauce. Serve with oranges; garnish with cilantro sprigs.