Preheat the oven to 425F/220C.
In a small pot, add brown sugar, smoked paprika, onion & garlic powder, thyme, salt, cayenne pepper, black pepper and olive oil and combine until a paste forms. Add a dash more oil if you need to loosen up the paste slightly.
Pat the drumsticks dry to remove excess moisture, then 'pull' the skin up to cover the meat (helps prevent the meat from drying out and keeps the skin crispy). Place in a large mixing bowl, and combine with the seasoning paste until everything is evenly coated.
Place a wire rack above a foil-lined baking tray. Use a brush to lightly brush the wire rack with oil to help prevent the chicken from sticking. Space the drumsticks out on the wire rack, ensuring the meatiest part with the most skin is facing up. Use a brush to collect all the leftover seasoning in the bowl and brush it over the drumsticks (you can add a dash of oil to the bowl if needed).
Bake in the oven for 35 minutes, or until crispy, lightly charred and piping hot right through the centre (a thermometer at the thickest part next to the bone should read 75C/165F). Timings will depend on the thickness of the thighs, so just be vigilant.