Preheat your oven to 400°F (200 °C) and line a large baking sheet with parchment paper for easy cleanup.
Pat the chicken drumsticks thoroughly dry with paper towels to ensure the skin gets a beautiful roast, then season them evenly with sea salt and black pepper.
In a small glass bowl, whisk together the honey, coconut aminos, avocado oil, minced garlic, and grated fresh ginger until well combined.
Arrange the drumsticks on the prepared baking sheet and brush them generously with half of the honey-garlic glaze.
Bake for 25 to 30 minutes, flipping the drumsticks halfway through and brushing with the remaining glaze until the chicken reaches an internal temperature of 165°F and the sauce is perfectly sticky.
While the chicken finishes roasting, place the broccoli florets in a steamer basket over boiling water and steam for 5 to 6 minutes until they are tender yet retain a crisp bite.
Plate the glazed drumsticks over the steamed broccoli, drizzling any extra pan juices over the top, and garnish with a sprinkle of sesame seeds.