Preheat your oven to 400°F. Line a rimmed baking sheet with high-heat-resistant parchment paper.
Wipe the chicken drumsticks dry with paper towels. Arrange them in a single layer on the baking sheet.
Prepare the rub: In a small bowl, combine the olive oil, kosher salt, chili powder, and cayenne pepper to create a paste. Pour the paste over the chicken pieces and, using your hands or a pastry brush, coat the chicken on all sides.
Bake the drumsticks until cooked through (their internal temperature should reach 165ºF) and juices run clear, for about 40 minutes. Check them after the first 30 minutes and loosely cover them with foil if they seem to be darkening too fast on top.
If you wish, garnish the chicken with chopped parsley and red pepper flakes, then serve.
Video
Notes
Sometimes I chop some fresh parsley and sprinkle it on top of the chicken pieces after baking. I also like to lightly sprinkle them with red pepper flakes. Both of these additions are purely optional.The leftovers keep well in the fridge, in an airtight container, for up to 4 days. Reheat them gently in the microwave, covered, at 50% power. Or simply eat them cold! They are delicious right out of the fridge, especially if prepared without the skin. It's no wonder cold chicken is the classic picnic food.