In a medium saucepan, heat the milk, heavy cream, and freshly brewed espresso over medium heat until it's almost simmering. Do not let it boil!
Add the honey and sugar, stirring until completely dissolved.
In a separate bowl, whisk the egg yolks until light and frothy. Slowly drizzle in a small amount of the warm milk-cream mixture to temper the yolks and prevent them from curdling.
Pour the yolk mixture back into the saucepan. Cook over low heat, stirring constantly, until the mixture thickens enough to coat the back of a spoon.
Remove from heat and stir in the cinnamon, ginger, cloves, vanilla extract, and a pinch of salt. Let cool completely.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.
When the ice cream is almost done churning, add the gingerbread crumbles to give the ice cream a crunchy texture.
Transfer the finished ice cream to an airtight container and freeze for at least 3 hours to achieve the desired consistency.
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