In a blender combine ketchup, worcestershire sauce, liquid smoke, soy sauce, hot sauce, brown sugar, cornstarch, salt, onion powder, oregano, basil, paprika, pepper, cayenne pepper, and garlic cloves.
Puree until smooth.
Brush sauce onto drumsticks.
Heat an outdoor grill to about 400 degrees. Put your drumsticks onto a well oiled grate. Sear on one side, flip, and brush on more barbecue sauce. Once the other side is seared, brush on more sauce and move to indirect heat. Reduce the heat to low.
Cook chicken to an internal temperature of 165 degrees F. Serve hot.
Be careful about cross contamination with the barbecue sauce. If you touch your chicken with a brush or spoon and then stick that utensil back into the bowl, the sauce is now contaminated. This means that the sauce cannot be eaten unless it has been cooked.