Heat the milk in a medium saucepan over medium-low heat until it just starts to simmer.

While the milk is heating, whisk the egg yolks in a medium bowl. Gradually add the hot milk to the egg yolks and whisk to combine. Gently stir in the honey.

Return the mixture to the saucepan and cook over medium-low heat, stirring constantly, until the mixture thickens and coats a wooden spoon.

Add the heavy cream and stir to combine. Strain the mixture through a fine-mesh strainer into a clean container. Cover with plastic wrap, pressing the plastic directly onto the surface of the mixture, and refrigerate overnight.

Pour the ice cream mixture into an ice cream maker and freeze according to the manufacturer's directions. Scoop the ice cream into bowls and top each serving with 1/3 cup sliced strawberries.