Preheat your oven to 425°F (220°C). Line a baking sheet with foil or parchment for easier cleanup, and place a rack on top if you have one. This helps air circulate and keeps the bottom from getting soggy.
Pat the drumsticks dry with paper towels. Dry skin will crisp better in the oven. Drizzle with olive oil and toss to coat evenly.
In a small bowl, combine salt, pepper, paprika (if using), minced garlic, and chopped parsley. Sprinkle over the drumsticks and rub well to season evenly.
In another bowl, mix grated Parmesan, panko breadcrumbs, and dried thyme or Italian seasoning. This will form the crunchy coating.
Dip each drumstick in the Parmesan mixture, pressing lightly to help the coating cling. Place the coated drumsticks on the prepared rack or baking sheet, skin side up.
Melt butter and drizzle a small amount over each drumstick. This helps create a glossy finish and a richer flavor.
Bake in the preheated oven for about 30–35 minutes, until the skin is golden and crisp and the internal temperature reaches 165°F (74°C). If you like extra crispiness, switch to broil for the last 1–2 minutes, watching closely to prevent burning.
If you want more garlic-forward flavor, you can brush a little more melted butter mixed with minced garlic over the drumsticks during the last few minutes of baking.
Remove from the oven and let rest for 5 minutes. Garnish with chopped parsley and a squeeze of lemon juice if desired. Serve warm.