For the ice cream:
1½ cups heavy cream
¾ cup plus 3 tbsp. sugar, divided
1½ tbsp. unsweetened cocoa powder
6 large egg yolks
1¼ cups buttermilk
1 tbsp. liquid red food coloring*
1 tsp. vanilla extract
For the cream cheese swirl:
4 oz. cream cheese, cold
2½ tbsp. unsalted butter, at room temperature
1¼ cups confectioners’ sugar, sifted
1 tbsp. vanilla extract
2 tbsp. heavy cream
In a medium saucepan, combine the heavy cream with ¾ cup of the sugar and the cocoa powder. Heat over medium-high heat, whisking occasionally, until warmed through and the sugar and cocoa have dissolved into the cream. Meanwhile, in a medium bowl or a large liquid measuring cup, combine the egg yolks and the remaining 3 tablespoons sugar. Whisk until smooth. Once the cream mixture is warm, slowly pour the mixture into the bowl with the egg yolks, whisking constantly to temper the eggs. Return the egg-cream mixture to the saucepan over medium high heat.
Cook the mixture, stirring constantly and scraping the bottom, until the mixture thickens and coats the spatula or spoon (about 170-175° F.) Pour the custard through the strainer into a bowl or storage container. Stir in the buttermilk, red food coloring, and vanilla. Cover and chill thoroughly in the refrigerator.
Just before you are ready to freeze the ice cream, make the cream cheese frosting. Combine the cream cheese and butter in the bowl of an electric mixer. Beat on medium-high speed until light and fluffy, about 2 minutes. Add in the confectioners’ sugar and mix on low speed just until incorporated. Blend in the vanilla and heavy cream. Increase the speed to medium-high and beat 2-3 minutes more. (It is not absolutely required, but putting the frosting in a pastry bag fitted with a large flat tip, such as Ateco #789, will make it easier to layer the frosting with the ice cream.)
Freeze the ice cream base in an ice cream maker according to the manufacturer’s instructions. Transfer to a storage container, alternating layers of ice cream with layers of frosting. Transfer to the freezer and freeze until firm.
*The red food coloring, in my opinion, is not totally crucial to the red velvet flavor so feel free to dial it down a bit if you are so inclined. However, I do think it is part of the flavor so I wouldn’t omit it entirely. Also keep in mind, the red color will look more pink/salmon colored immediately after freezing in the ice cream maker, but don’t be tempted to add more coloring. The color will return to a deep red after fully freezing.