Preheat the oven to 425°F (220°C) and line a baking sheet with parchment paper.
Place the chicken drumsticks on the prepared baking sheet in a single layer.
Brush each drumstick with the melted butter, then evenly season with smoked paprika, garlic powder, sea salt, black pepper, and the chopped rosemary leaves.
Bake for 20 minutes, then flip the drumsticks and bake for an additional 10 minutes.
Check the internal temperature in the thickest part of a drumstick; it should read at least 165°F (74°C).
Remove from the oven and let the drumsticks rest for 5 minutes before serving.