Beat the sugar and cream cheese together until smooth and creamy. Beat in the egg and vanilla. Set aside.
Bring the milk to a boil in a heavy medium saucepan. Slowly beat the hot milk into the cheese mixture.
Pour the entire mixture back into the pan and place over low heat. Stir constantly with a whisk or wooden spoon until the custard thickens slightly. Be careful not to let the mixture boil or the egg will scramble.
Remove from the heat and pour the hot cheese custard through a strainer into a large bowl. Allow the custard to cool slightly, then stir in the heavy cream. Cover and refrigerate overnight.
Stir the chilled custard, then freeze in your ice cream machine according to the manufacturers instructions, adding the crumbled Oreo cookies when the ice cream is semifrozen.
Allow the machine to mix in the cookies. When finished, the ice cream will be soft but ready to eat. For firmer ice cream, transfer to a freezer-safe container and freeze for at least 2 hours.
