Start by heating your oven to 425°F (218°C) and set up a baking tray with parchment paper or place a wire rack on a baking sheet. Make sure to thoroughly dry the chicken drumsticks with paper towels to keep them crispy.
Combine the olive oil, smoked paprika, garlic powder, onion powder, dried oregano, salt, black pepper, and optional cayenne pepper in a bowl and whisk until evenly mixed. Transfer the drumsticks to a large bowl and rub the spice mixture all over each piece, ensuring full coverage.
Arrange the drumsticks on the tray or wire rack without letting them touch, allowing air to flow freely around each drumstick for even crisping.
Place the tray in the preheated oven and bake for about 35 to 45 minutes. Flip the drumsticks halfway through cooking to promote even browning. The drumsticks are done when they reach an internal temperature of 165°F (74°C), but cooking to 175°F (79°C) will yield even more tender meat.
Take the drumsticks out of the oven and let them rest for 5 minutes to let the juices settle, which keeps the meat juicy and flavorful before serving.