Preheat oven to 425°F (220°C). Line a baking sheet with foil and place a rack on it if you have one.
Pat drumsticks dry and put them in a large bowl. Drizzle with olive oil and toss to coat.
Whisk spices and brown sugar in a small bowl, then sprinkle over the chicken. Toss until evenly coated.
Arrange drumsticks on the rack, leaving space between pieces. Bake 30–35 minutes, turning once, until internal temp reaches 165°F (74°C).
If you want a bit more color, broil 2–3 minutes, watching closely to avoid burning. Let rest 5 minutes before serving.