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