Melt the butter in a saucepan, then add the finely chopped apples, cinnamon, nutmeg, and 30g of sugar. Sauté over medium heat until the apples soften and caramelize. Then, let it cool completely.
In a saucepan, heat the milk and heavy cream over medium heat until it almost reaches a simmer. Do not let it boil!
Meanwhile, in a separate bowl, whisk the egg yolks with the remaining sugar until light and creamy.
Gradually, while whisking constantly, add a small amount of the warm milk mixture to the egg yolk mixture to temper the eggs and prevent them from curdling.
Pour the entire mixture back into the saucepan and cook over low heat, stirring constantly, until it thickens enough to coat the back of a spoon.
Remove from the heat, then stir in the vanilla extract and a pinch of salt. Let it cool completely.
Gently fold the cooled apple mixture into the ice cream base, ensuring the apple pieces are evenly distributed.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.
When the ice cream is almost completely churned, add the crushed cookies or pie crust pieces to capture the characteristic flavors of apple pie.
Transfer the finished ice cream to a sealable container and freeze for at least 3 hours to achieve the desired consistency.
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