In a 9×13-inch casserole dish, whisk together olive oil, sesame oil, honey, soy sauce, minced garlic, grated ginger, and black pepper until combined.
Add the chicken drumsticks to the dish and toss to coat each piece evenly in the marinade.
Cover the dish with plastic wrap and refrigerate to marinate for at least 2 hours or up to overnight.
Preheat the oven to 375°F (190°C).
Remove the plastic wrap and place the dish in the preheated oven. Bake the drumsticks for about 45 minutes, turning once halfway through to promote even browning.
Cook until an instant-read thermometer inserted into the thickest part of a drumstick registers 175°F (79°C).
Remove from the oven, spoon any pan sauce over the drumsticks, garnish with chopped parsley, and serve.