To one small zippered bag add cream, milk, sugar and vanilla. Remove as much air as possible and seal.
Now place this first bag into the second small zippered bag. This will help prevent any salt water from contaminating the ice cream.
Pour the ice cubes and rock salt into the large zippered bag, then add the double-bagged ice cream base into the large bag. Remove the air from the bag and seal.
Wrap everything in two layers of dish towels and place the completed bundle into the large shopping bag, tying with a rubber band.
Shake and throw the bag for 15 minutes, or until the ice cream becomes solid.
Carefully remove the ice cream bag from the salty water, wiping off any excess salt water. Open the inner bag and serve ice cream.