Preheat oven to 425°F (220°C). Pat the poultry completely dry with paper towels to ensure the skin crisps up properly.
Rub the meat evenly with olive oil. In a small bowl, mix the Kosher salt, black pepper, garlic powder, and paprika, then season generously on all sides.
Place the seasoned pieces skin-side up on a baking sheet lined with foil or parchment paper. Tuck the fresh rosemary sprigs underneath.
Bake for 35 to 45 minutes, or until an instant-read thermometer inserted into the thickest part of the meat reads 165°F (74°C).
Remove from the heat and let rest for 5 to 10 minutes before slicing to allow the juices to redistribute.