Preheat oven to 425°F (220°C). Line a large baking sheet with aluminum foil and set a wire rack on top. Pat drumsticks completely dry with paper towels – this ensures crispy skin.
In a small bowl, combine melted butter, olive oil, minced garlic, rosemary, smoked paprika, salt, pepper, and baking powder. Stir until a thick paste forms.
Place drumsticks in a large mixing bowl. Pour the herb butter mixture over them and toss with your hands, making sure every drumstick is evenly coated. Let sit for 5 minutes while the oven finishes heating.
Arrange drumsticks on the wire rack, leaving space between each for air flow. Bake for 40–45 minutes, flipping drumsticks halfway through, until skin is deep golden brown and internal temperature reaches 165°F (74°C).
For extra shatteringly crispy skin, switch the oven to broil on high for 1–2 minutes, watching carefully. Remove from oven and let rest on the rack for 5 minutes before serving.