Add all the ingredients for the ice cream base to a high-powered blender and pulse until smooth.
8 ounces cream cheese, 1 cup heavy cream, 1 cup whole milk, 3-4 teaspoons red liquid food coloring, ¾ cup granulated sugar, 1 tablespoon unsweetened cocoa powder, ¼ teaspoon salt
Pour the ice cream base into a large bowl and chill for at least 2 hours (up to overnight).
Pour the chilled ice cream mixture into an ice cream maker (follow the instructions for your ice cream machine model).
In an electric mixer, combine the cream cheese butter, and vanilla extract.
½ cup unsalted butter, 4 ounces cream cheese, 2 cups powdered sugar, 1 teaspoon vanilla extract
Beat in the powdered sugar a little bit at a time until the mixture is light and fluffy.
When the ice cream is ready, pour half into a loaf pan or other freezer-safe container.
Add a layer of cream cheese swirl on top and use a knife to swirl it into the ice cream.
Add the rest of the ice cream on top and then swirl in the rest of the cream cheese icing.
Cover with plastic wrap and freeze overnight.