How to Make It
Heat oven to 450° F with a rack in the highest position. Cook the rice according to the package directions.
Meanwhile, in a small bowl, mix together the ginger, garlic, and ½ teaspoon salt. Place the chicken on a rimmed baking sheet. Loosen the skin and, dividing evenly, spread the ginger mixture underneath. Rub the outside of the chicken with 1 tablespoon of the oil. Bake until the skin is golden and a thermometer inserted in the thickest part of a thigh registers 165° F, 15 to 20 minutes.
Heat the remaining 2 tablespoons of oil in a large skillet over medium-high heat. Add the bok choy, broccoli, and ¼ cup water. Cover and cook, tossing occasionally, until the vegetables are tender, 6 to 8 minutes. Pour off any water from the pan, add the soy sauce and sesame seeds, and toss to combine. Serve with the chicken and rice.