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