Start the smoke tube so that you have a steady smoke.
Place the cheese on the smoker along with a bowl of ice. Place the lid on the grill.
Rotate and turn the cheese to ensure the smoke flavor is even, about every 15 minutes.
After at least an hour of smoking, your cheese is done.
You can serve the smoked cheddar or smoked mozzarella immediately or keep it in the refrigerator for up to two weeks.
Storage: Store the smoked cheese in the refrigerator in an airtight container. You can also wrap it tightly in plastic wrap, but sometimes the smell of the smoke can fill the fridge if not wrapped well.