Gooey Butter Cake Ice Cream

Cream, nonfat milk, cane sugar, butter cake [eggs gluten free flour (brown rice flour, tapioca starch, white rice flour, potato starch, sorghum flour, arrowroot starch, sweet rice flour, guar gum), sugar, brown sugar, butter, egg yolks, madagascar bourbon vanilla extract, baking powder (monocalcium phosphate, sodium bicarbonate, corn starch), sea salt], gooey butter sauce [cream, brown sugar, sugar, honey, butter, sea salt, lemon juice], cream cheese, (cultured milk and cream, salt, xanthan gum, carob bean and/or guar gum), tapioca syrup, tapioca starch, sea salt, madagascar bourbon vanilla extract, natural flavor.