Preheat the oven to 425°F (220°C).
Pat the drumsticks dry with paper towels and season them evenly with the salt and black pepper.
In a small skillet, heat the olive oil over medium heat.
Add the minced garlic, smoked paprika, red pepper flakes, chopped parsley, and chopped oregano to the hot oil and cook, stirring, for about 1 minute—do not let the garlic burn.
Pour the spiced oil mixture over the seasoned drumsticks and use tongs or your hands to coat each piece thoroughly.
Arrange the coated drumsticks in a 9×13-inch baking dish in a single layer.
Bake for about 45 minutes, until the drumsticks are cooked through and the juices run clear; an instant-read thermometer should read at least 165°F (74°C).
Remove from the oven and let rest briefly before serving with your favorite side or salad.