Preheat oven to 425 degrees F. Place chicken on a large rimmed baking sheet. Brush with 1 tsp. oil and sprinkle with 1/2 tsp. garlic powder and 1/8 tsp. salt. Roast for 15 minutes.
Meanwhile, toss green beans with the remaining 3 tsp. oil, 1/4 tsp. garlic powder, and 1/8 tsp. salt in a large bowl.
After the chicken has roasted for 15 minutes, add the beans to the baking sheet in an even layer around the chicken. Brush hoisin sauce over the chicken. Return to the oven and roast until an instant-read thermometer inserted in the thickest part of the chicken without touching the bone registers 165 degrees F and the beans are tender and beginning to brown, 10 to 15 minutes more.
Combine sesame seeds and scallion in a small bowl. Toss half of the sesame seed mixture with the beans and sprinkle the remaining sesame seed mixture over the chicken.
Tip: Toasting sesame seeds enhances their naturally nutty flavor. You can buy toasted sesame seeds in the spice aisle or toast raw seeds yourself. To toast the seeds, cook in a small dry skillet over medium-low heat, stirring constantly, until fragrant and lightly browned, 2 to 4 minutes.