Vanilla flavored ice cream with cookie dough pieces

Skim milk, sugar, cookie dough (wheat flour, dark fudge chips [sugar, coconut oil, cocoa [processed with alkali], fully hydrogenated coconut oil, cocoa, salt, soy lecithin, natural vanilla flavor], sugar, brown sugar [sugar, molasses], margarine [soybean oil, palm oil, water, salt, vegetable mono - and diglycerides, soy lecithin, sodium benzoate {preservatives}, natural butter flavor, annatto {for color}, vitamin a palmitate added], chocolate chips [sugar, chocolate liquor, cocoa butter, soy lecithin], water, natural vanilla flavor, salt, baking soda, corn starch), cream, corn syrup, contains 2% or less of: whey protein isolate, guar gum, mono - and diglycerides, tara gum, cellulose gum, polysorbate 80, xanthan gum, vitamin a palmitate, carrageenan, dextrose and tapioca starch, natural vanilla flavor, annatto (for color).