1. Preheat your oven to 400°F (200°C). Place an oven rack in the middle position and another above it. Line a baking tray with parchment paper or lightly grease it.
2. In a small bowl, mix olive oil, smoked paprika, garlic powder, onion powder, cumin, salt, and pepper. Rub this mixture all over the chicken drumsticks.
3. Prepare the potatoes by tossing them with olive oil, oregano, paprika, salt, and pepper. Spread them out evenly on the prepared baking tray.
4. Position the chicken drumsticks by hanging them on the top oven rack using the thick end of the drumstick through the rungs. Place the baking tray with the potatoes directly below to catch the drippings from the chicken.
5. Roast for 40-45 minutes, flipping the potatoes halfway through, until the drumsticks are cooked through (internal temperature of 165°F/74°C) and the potatoes are golden and crispy.
6. Remove from the oven, serve the drumsticks with the roasted potatoes, and enjoy a perfectly juicy and flavorful meal.