Vanilla Ice Cream with Chocolate Sandwich Cookie Pieces

milk, cream, buttermilk, cookies sugar, enriched flour white flour, niacin, iron, thiamine mononitrate, riboflavin, folic acid, vegetable oil contains hydrogenated canola, and cottonseed oil, cocoa, coconut oil, corn starch, brown sugar syrup, salt, sodium bicarbonate, nonfat dry milk, whey, soy lecithin, ethyl maltol, natural and artificial flavors, corn syrup, high fructose corn syrup, sugar, whey, stabilized and emulsified by mono and diglycerides, guar gum, locust bean gum, cellulose gum, and carrageenan, artificial flavor, and vegetable annatto color