Set your oven to 425°F (218°C) and prepare a large baking sheet by lining it with parchment paper or placing a wire rack on a tray.
Dry the chicken drumsticks thoroughly with paper towels to ensure maximum crispiness.
Combine the olive oil with all spices—including smoked paprika, garlic powder, onion powder, dried oregano, salt, black pepper, and cayenne if using—in a small bowl.
Toss the chicken drumsticks in the seasoned oil mixture, coating each piece evenly by massaging it into the skin.
Arrange the drumsticks on the prepared pan so they are spaced apart and not touching; use a wire rack if possible to promote even airflow.
Cook the chicken in the preheated oven for 35 to 45 minutes, flipping the drumsticks halfway through to cook evenly on both sides.
Check that the internal temperature reaches at least 165°F (74°C), or up to 175°F (79°C) for even more tender meat.
Allow the drumsticks to sit for 5 minutes after baking to let the juices settle before serving.