Preheat the oven to 425°F. Spray a baking sheet with nonstick cooking spray and set aside.
Pat the chicken legs dry with paper towels so the skin crisps up, then transfer them to a large bowl or a sealable plastic bag.
In a small bowl, mix the olive oil, salt, and spices into a paste. Add it to the drumsticks, then seal the bag (or cover the bowl) and shake until the chicken is evenly coated.
Place the drumsticks on the baking sheet and bake for 40 to 45 minutes, flipping them halfway through, until the internal temperature reaches 165°F.
For extra-crispy skin, place the drumsticks under the broiler for a few minutes at the end, watching closely so they don't burn.
Let the chicken rest for five minutes, then sprinkle with the chopped parsley and serve.