To make the sauce: In a saucepan, stir all the sauce ingredients together using a whisk.
Bring mixture to a boil; lower heat to medium-low and simmer for 20 minutes or so, until the apples are cooked and the sauce is thickened.
Throw out the cinnamon stick; let sauce cool for 5 minutes.
Puree sauce in a blender or food processor.
Equally divide sauce into 2 bowls; set aside.
To make rub: In a bowl or heavy duty plastic zip-top bag add all the rub ingredients; stir or shake to combine.
Rinse the turkey legs under cold water and pat dry.
Coat turkey legs with rub mixture; let stand for 20 minutes at room temperature before grilling.
Spray or lightly brush turkey legs with vegetable oil.
Follow your grill manufacturer's instructions for using wood chunks.
Grill turkey legs over indirect medium heat for approximately 1 hour or until meat thermometer reads 180° when inserted into the thickest part of the meat (baste occasionally with sauce from 1 reserved bowl).
Take legs off grill and served with sauce from the 2nd reserved bowl.