Beat the egg yolks and honey together in a medium bowl, and set aside.
Heat the milk in a saucepan until it reaches boiling point, then simmer. While it's simmering stir in the egg yolks and honey mixture. Continue to stir until it thickens, and coats the back of a wooden spoon.
Remove from the heat, strain and leave to cool.
Stir in the cream and the vanilla, and transfer the mixture into an ice cream maker. Follow the manufacturer's instructions.