In a medium bowl, whisk together shallot, honey, stone-ground mustard, Dijon mustard, heavy whipping cream, rosemary, lemon juice, salt, and pepper.
Reserve half of the marinade in a separate bowl and refrigerate for basting later.
Add the other half of the marinade to a Ziploc bag or large bowl with the chicken drumsticks. Toss to coat. Cover and refrigerate for at least 1 hour.
Remove the chicken from the fridge 10-15 minutes before grilling. Shake off excess marinade.
Preheat a grill pan over high heat for 2 minutes, then reduce to medium-high. Add 1 tablespoon olive oil and spread it with a brush.
Add drumsticks and grill for 8 minutes. Flip and grill for another 8 minutes. Flip again and grill for 8-10 more minutes.
Brush with reserved marinade and grill an additional 1-2 minutes or until the internal temperature reaches 165°F.
Serve with lemon wedges and rosemary sprigs for garnish.