Place the butter in a microwave-safe glass liquid measuring cup or bowl and microwave for 30 seconds or until melted. Add the honey, dijon mustard, whole grain mustard, salt, and pepper and stir to combine. (If you're using dried thyme, add it here.)
Arrange the drumsticks in a single layer on the bottom of the slow cooker insert. (It works well to alternate the direction each one faces so they all fit nicely together.)
Pour the sauce over the drumsticks. Top with the fresh thyme.
Cover and cook on high for 3-4 hours, or low for 5-6 hours.
Just before serving, preheat the oven to broil. Transfer the drumsticks to a baking dish and pour the sauce over the top. Broil for about 5 minutes, or until the tops are goldenbrown and the skin begins to crisp up. Serve immediately.
