Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Pat the chicken drumsticks thoroughly dry with paper towels to ensure the skin becomes perfectly crispy during roasting.
Peel the sweet potato and cut it into 1-inch cubes, and chop the broccoli into uniform, bite-sized florets.
In a large mixing bowl, combine the chicken, sweet potato cubes, and broccoli florets.
Drizzle with olive oil and sprinkle with garlic powder, rosemary, thyme, sea salt, and black pepper, tossing well to coat everything evenly.
Spread the mixture in a single layer on the prepared baking sheet, making sure the chicken pieces are not crowded.
Roast for 25 to 30 minutes, tossing the vegetables halfway through, until the chicken reaches an internal temperature of 165°F and the potatoes are tender.
Remove from the oven and let the chicken rest for 5 minutes before serving to keep the meat juicy.