Prepare the grill for indirect cooking over high heat (450° to 550°F).
In a small bowl mix the rub ingredients.
Using poultry shears cut along both sides of each backbone and discard them. Turn the hens over, with the skin side facing up, and press with the palms of both hands to crack the rib bones and flatten the hens.
Lightly coat the skin of each hen with oil and season evenly with the rub. Set aside while making the glaze.
In a small saucepan combine the glaze ingredients and bring to a boil over high heat on the stove. Lower the heat and simmer, stirring occasionally, until the glaze begins to thicken, 5 to 7 minutes. Whisk in the butter, remove from the heat, and set aside.
Brush the cooking grates clean. Grill the hens, skin side down first, over direct heat, with the lid closed, until the skin is golden brown, 8 to 12 minutes, turning once, being careful not to tear the skin.
Slide the hens over indirect high heat and cook, skin side up, for 15 to 20 minutes. Brush the skin with a thin layer of the glaze, using just enough so it doesn’t drip into the grill. Continue to cook until the juices run clear and the internal temperature reaches 160° to 165°F in the thickest part of the thigh (not touching the bone), 5 to 15 minutes more, brushing every 5 minutes with the glaze. Keep the lid closed as much as possible during grilling.
Transfer the hens to a cutting board. Brush with the glaze and let rest for about 5 minutes (the internal temperature will rise a few degrees during this time). Cut each hen in half lengthwise along the breastbone. Serve warm with additional glaze on the side, if desired.