Combine the oil, Italian seasoning, garlic powder, and sea salt in a large resealable plastic bag or mixing bowl.
Add the drumsticks to the bag or bowl, seal or cover, and shake or toss until all pieces are evenly coated with the seasoning mixture.
Refrigerate the coated drumsticks for at least 15 minutes, or ideally several hours and up to 24 hours, to marinate.
When ready to cook, preheat the oven to 450°F (230°C).
Arrange the marinated drumsticks in a single layer on a rimmed baking sheet or roasting pan; line the sheet with parchment or foil or spray it if desired to prevent sticking.
Bake for about 20 minutes, until the chicken is golden brown and cooked through.
For crispier skin, move the baking sheet to the second-from-top oven rack and broil for 5 to 8 minutes, watching closely to avoid burning.
Remove the drumsticks from the oven, drizzle each with 2 to 3 tablespoons of honey total (adjust to taste), and serve.