Preheat oven to 350°F. Heat 1 tablespoon oil in a large ovenproof skillet over medium-high heat. Add chicken, skin-side down; cook, undisturbed, until the skin is golden brown and crisp, 8 to 10 minutes. Transfer the chicken, skin-side up, to a large plate. Remove skillet from heat; reserve 1 tablespoon of the drippings in the skillet (discard remaining drippings).
Meanwhile, whisk 1 tablespoon orange zest, ¾ cup orange juice, 2 tablespoons soy sauce, 2 teaspoons sugar, 2 teaspoons ginger, 1⅛ teaspoons salt, 1 teaspoon cornstarch and ¼ teaspoon pepper in a medium bowl until combined. Pour ½ cup of the mixture into a small saucepan.
To the reserved drippings in the skillet, add 2 (8.8-ounce) packages brown rice, 6 cups broccoli and the remaining ½ cup orange juice mixture and ½ teaspoon cornstarch; stir until well combined. Nestle the chicken, skin-side up, into the broccoli mixture.
Bake until the broccoli is tender, the sauce has thickened slightly, and an instant-read thermometer inserted into the thickest portion of chicken registers at least 165°F, 35 to 40 minutes.
Meanwhile, bring the reserved orange juice mixture in the saucepan to a simmer over medium heat. Simmer, stirring occasionally, until the sauce thickens and coats the back of a spoon, about 5 minutes. Spoon the sauce over the chicken. Sprinkle with scallions and sesame seeds.