1. In the bowl of an electric mixer fitted with the whisk attachment, whisk the honey and egg yolks on medium speed until the mixture is thick and light, 5 to 7 minutes. In a small saucepan, bring milk to a boil over high heat.

2. Add half the milk to the egg mixture, and beat to combine. Transfer all the egg mixture to the saucepan with the remaining milk. Place saucepan over medium heat. Cook, stirring constantly with a wooden spoon, until the mixture thickens so that a finger leaves a trail when it is dragged across the mixture as it coats the back of spoon, about 5 minutes. Do not allow mixture to boil, or it will curdle.

3. Remove from heat and immediately stir in heavy cream.

4. Transfer the mixture to a metal bowl set in an ice-water bath and chill, stirring occasionally. Stir in vanilla. Transfer the mixture to an ice-cream maker, and freeze according to manufacturer's instructions.