Preheat the oven to 400°F (200°C). Line a baking sheet with aluminum foil and place an oven-safe rack on top; lightly spray the rack with olive oil cooking spray.
Pat the drumsticks dry with paper towels to remove excess moisture.
In the first shallow bowl, combine the all-purpose flour and dried oregano.
In the second bowl, beat the eggs until smooth.
In the third bowl, mix the panko breadcrumbs with dried basil, garlic powder, onion powder, smoked paprika, salt, and black pepper.
Working one drumstick at a time, dredge it in the flour mixture, shake off excess, dip it in the beaten eggs, then press it firmly into the seasoned panko so the crumbs adhere evenly.
Place the breaded drumsticks on the prepared rack, spaced apart. Lightly spray the drumsticks with olive oil cooking spray.
Bake in the preheated oven for 45 minutes, turning once halfway through, until the drumsticks are cooked through and reach an internal temperature of 165°F (74°C).
Remove from oven and let rest a few minutes before serving.