In a medium bowl, whisk together the shallot, honey, stone-ground mustard, Dijon mustard, heavy whipping cream, fresh rosemary, lemon juice, salt, and black pepper until smooth. Transfer half of the marinade to a separate bowl, cover, and refrigerate to use later for basting.
Add the remaining marinade to a large zip-top bag or shallow dish. Add the chicken drumsticks and turn to coat evenly. Cover and refrigerate for at least 1 hour. Remove the chicken from the refrigerator 10 to 15 minutes before grilling and gently wipe off any excess marinade.
Preheat a grill or grill pan over high heat for 2 minutes. Reduce the heat to medium-high and lightly oil the grates or pan.
Place the drumsticks on the hot grill or grill pan and cook for 8 minutes. Flip and cook for another 8 minutes, then flip once more and continue cooking for 8 to 10 minutes, turning as needed, until the chicken is browned and cooked through.
Brush the reserved marinade over the drumsticks during the final 1 to 2 minutes of cooking. Continue cooking until the internal temperature reaches 165°F.
Remove from the grill or grill pan and serve immediately with lemon wedges and fresh rosemary, if desired.