Combine the heavy cream and milk in a large sauce pan over medium heat. Bring to a simmer, but do not boil.
Meanwhile, beat together the egg yolks and sugar until the mixture is light and lemony in color. Add the cream cheese, and beat until the mixture is smooth. While mixing, gradually add in about 1 cup of the hot cream. This will temper the eggs.
Add the tempered egg and cream cheese mixture to the sauce pan, and continue to cook, stirring continuously, until the mixture thickens and coats a spoon. Add vanilla. Remove from heat.
Allow the ice cream base to cool slightly, then cover with plastic wrap and refrigerate until cold. At least 2 hours but longer is better.
Freeze in your ice cream maker.
While ice cream is in the maker, breakup cupcakes into small small pieces. This depends on if you want big chunks or small pieces in your ice cream.
Fold cupcake pieces into ice cream and seal in container.