In a bowl, beat the sugar and cream cheese until smooth and creamy; beat in the egg and vanilla; set aside.
Bring the milk to a boil in a 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 (don’t let the mixture boil or the egg will scramble).
Remove pan from heat and pour the hot custard through a strainer into a large clean bowl.
Let the custard cool slightly, then stir in the lemon zest and cream.
Cover and refrigerate until cold or overnight.
Stir the chilled custard; freeze in 1 or 2 batches in an ice cream maker according to the manufacturer’s directions, adding the crumbled graham crackers to the machine when the ice cream is semifrozen; allow the machine to mix in the crackers.
When finished, the ice cream will be soft but ready to eat.
For firmer ice cream, transfer mixture to a freezer-safe container and freeze several hours.
*White Chocolate Cheesecake Ice Cream: omit the lemon zest; add ½ cup melted white chocolate to the custard along with the vanilla; proceed as directed.
*Oreo Cheesecake Ice Cream: omit the lemon zest; substitute crumbled oreos for the graham crackers; proceed as directed.