"This is one of my favorite recipes. My Mom, Lucy Wahnsiedler, used to make this when I was a kid. I love the flavor of the spread, and it is marvelous for making sandwiches or for spreading on crackers. It is simply delicious!"
Place ham into a saucepan and cover with water. Bring to a boil, reduce heat to medium, and boil ham gently for 15 minutes. Drain and allow ham to cool.
Place ham into a food processor and pulse several times to grind the meat to your desired texture.
Stir tomato sauce, tapioca, ketchup, mustard, vinegar, and Worcestershire sauce in a large saucepan over low heat; melt cheese food in the tomato sauce mixture and stir all ingredients smoothly together. Do not allow to simmer.
Combine melted cheese food mixture with ground ham in a large bowl; stir thoroughly. Chill before serving.