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Heat the milk, cream, sugar, and allspice until just about to boil.
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Whisk the egg yolks together in a heatproof bowl.
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Slowly pour the cream mixture into the yolks, whisking quickly to temper the eggs.
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Strain the tempered mixture back into the pan.
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Reheat the mixture, stirring occasionally until it thickens. It should coat the back of a wooden spoon.
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Remove from heat and strain into a heatproof bowl.
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Cover with plastic wrap. Make sure the wrap touches the top of the mixture.
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Refrigerate for at least 3 hours or overnight.
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Transfer mixture to the bowl of an ice cream maker and process according to the manufacturer's directions.
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When ice cream reaches soft serve consistency, mix in the chocolate chips.
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Transfer the ice cream to a freezer-proof container.
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Freeze for 1-2 hours until it hardens.