In a medium saucepan with high sides, heat the heavy cream, milk and honey on medium heat until it simmers (do not let it boil).
Meanwhile, put the egg yolks in a small bowl and set aside.
Once the milk mixture comes to a simmer, pour about 1/2 cup of it into the bowl with the egg yolks. Whisk vigorously until the mixture is uniform. Then slowly pour it back into the saucepan and continue to whisk until everything is well incorporated. The mixture should thicken after a few minutes and coat the back of your spoon or spatula.
Add in the vanilla extract and mix well.
Transfer the mixture to a large container and allow it come to room temperature. Then chill it in the refrigerator until it is completely cool.
Churn the ice cream in an ice cream maker according to the manufacturer's directions. Then transfer the ice cream to a freezer-safe container and place in the freezer to firm up.