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Break up the chocolate and place it, with the milk and honey in a heavy saucepan over medium heat.
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Scrape the bottom and sides constantly with a rubber spatula until the chocolate is melted and then whisk the mixture until smooth.
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Meanwhile, place the yolks in a stand mixer bowl and beat to mix.
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Gradually add the sugar and beat until the mixture becomes slightly pale.
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Then, very slowly and on low speed, add the warm chocolate mixture and beat until smooth; it will be thick.
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Transfer the mixture to a large heavy saucepan; cook over low heat, you must scrape the bottom and sides constantly with a large wide rubber spatula, until the mixture reaches 140° on a candy thermometer.
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Gradually whisk in the cream; stir occasionally until cool.
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Chill in the freezer or refrigerator until very cold, and then freeze in an ice cream maker according to manufacturer’s directions.