Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Peel and cube the sweet potato into half-inch pieces so they cook at the same rate as the chicken.
In a large mixing bowl, combine the chicken drumsticks, cubed sweet potatoes, and broccoli florets.
Mince the garlic and add it to the bowl along with the olive oil, rosemary, thyme, sea salt, and black pepper.
Toss everything thoroughly until the chicken and vegetables are evenly coated in the oil and herb mixture.
Spread the mixture onto the prepared baking sheet in a single layer, ensuring there is space between the pieces for even roasting.
Roast in the oven for 25 to 30 minutes, flipping the drumsticks halfway through, until the chicken reaches an internal temperature of 165°F.
Remove from the oven and let the chicken rest for 3 minutes before serving alongside the roasted vegetables.