In a medium saucepan, heat the milk and heavy cream over medium heat until it's almost simmering. Do not boil!
In a separate bowl, whisk together the egg yolks and sugar until light and creamy.
Gradually whisk a small amount of the warm milk mixture into the egg yolk mixture to temper the eggs and prevent curdling.
Pour the entire mixture back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens slightly and coats the back of a spoon.
Remove from the heat and stir in the lemon juice, lemon zest, vanilla extract, and a pinch of salt. Let it cool completely.
In a bowl, beat the cream cheese until smooth, then gently fold in the cooled lemon mixture until well combined and smooth.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.
When the ice cream is almost finished churning, add the crushed graham crackers to mimic the cheesecake texture.
Transfer the ice cream to a freezer-safe container and freeze for at least 3 hours, or until firm.
Let it sit at room temperature for a few minutes before serving to soften slightly for easier scooping.
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