In a saucepan over low heat, whisk together coconut milk and honey until warm.
Place egg yolks in a separate bowl. Whisking continuously, slowly ladle in about half of the coconut milk mixture. Transfer the egg mixture to the pan and heat over low heat, stirring constantly, until it coats the back of a wooden spoon, about 8 minutes.
Strain through a mesh strainer into a mixing bowl. Refrigerate until chilled, preferably overnight.
Once chilled, transfer to a blender and add strawberries. Blend until smooth (or leave strawberry chunks if desired).
Freeze in ice cream maker according to manufacturer’s instructions. Transfer to freezer-safe container and freeze up to 1 week.
(For best results, let sit at room temperature for 5 - 10 minutes before scooping and serving.)