Break the white chocolate into smaller pieces and set aside.
In a saucepan, combine the heavy cream, milk, and sugar. Heat over medium heat until the sugar is completely dissolved. Do not boil.
In a separate bowl, whisk the egg yolks. Gradually whisk in a small amount of the warm milk mixture to temper the eggs (prevent curdling).
Pour the egg yolk mixture back into the saucepan. Cook over low heat, stirring constantly, until the custard thickens and coats the back of a spoon.
Remove from the heat and add the chopped white chocolate. Stir until completely melted and the mixture is smooth.
Stir in the vanilla extract, then let it cool completely to room temperature.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions. If you don't have an ice cream maker, pour it into a freezer-safe container and stir it every hour during the freezing process.
Freeze for at least 4-5 hours, or until firm. Let it sit at room temperature for a few minutes before serving.
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