Preheat the oven to 425°F (220°C) and line a large baking sheet with parchment paper or lightly grease it.
Pat the chicken drumsticks dry with paper towels.
In a small bowl, combine garlic powder, onion powder, paprika, thyme, salt, and black pepper.
Rub the chicken with 1 tablespoon of olive oil, then coat evenly with the seasoning mixture.
Place the drumsticks on one side of the baking sheet.
Toss the carrots with the remaining olive oil and spread them on the other side of the pan.
Roast for 25 minutes.
Remove the pan from the oven and drizzle the honey over the carrots. Toss gently to coat.
Return the pan to the oven and roast for another 15–20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the carrots are tender and lightly caramelized.
Let the chicken rest for 5 minutes before serving.
Garnish with chopped parsley if desired and serve warm.