Rinse each Cornish game hen and pat dry with a paper towel.
Pull the skin away from the breast meat using your finger, being careful not to tear it.
Put ½ tbsp butter on each side of breast meat in each bird.
Place half a sprig’s worth of rosemary in along with the butter.
Place ¼ tsp of thyme in along with the butter.
Coat each bird with a dry rub.
Cover with plastic and place in refrigerator for at least one hour.
Prepare smoker to 275°F.
Arrange Cornish game hens on grates and close the smoker.
Cook hens to 160°F internal temperature at the thickest part of breast and thigh.
Increase smoker temperature to 300°F.
Glaze each bird with BBQ sauce - optional.
Continue to glaze the hens until their internal temperature reaches 165°F.
Remove from smoker, tent with foil and let rest at least 15 minutes.
Serve whole or carved.