Prepare glaze: In a small saucepan, place first 6 ingredients (honey through water); bring mixture to a boil, stirring until honey has dissolved.
Reduce heat and simmer until mixture has reduced and is thick and syrupy (7 to 8 minutes); strain and set aside.
Preheat oven to 400 degrees. Drizzle drumsticks with olive oil, season with salt and pepper then place them on a foillined baking sheet; bake for 45 minutes or until golden and cooked through. Remove from oven, drizzle with glaze and toss to coat.
Return to oven; bake for 8 to 10 minutes or until glaze has started to caramelize. Cool drumsticks for at least 10 minutes before serving.