In a saucepan, heat the milk and heavy cream over medium heat until warm, but do not boil. Stir in the honey, cinnamon, nutmeg, ground ginger, and ground cloves. Let it warm for 5 minutes.
In a separate bowl, whisk the egg yolks and sugar together until light and creamy.
Slowly pour a small amount of the hot milk mixture into the egg yolk mixture, whisking constantly to temper the eggs.
Pour the egg mixture back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens and coats the back of a spoon. Do not boil!
Remove from the heat, add the vanilla extract, and let it cool completely. Refrigerate for at least 4 hours or overnight.
Pour the chilled ice cream base 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 whisk with a fork every hour to maintain a creamy texture.
When the ice cream is partially frozen, add the coarsely crushed gingerbread cookies and gently fold them in, being careful to keep them crunchy.
Return to the freezer and let it freeze completely. Before serving, let it sit at room temperature for a few minutes to soften slightly.
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