Whisk coconut milk, milk, and 1 cup sugar in a saucepan until combined.

Bring the mixture to a boil over medium heat.

In a separate bowl, dissolve cornstarch in water.

Reduce the heat on the milk mixture to low.

Whisk in the cornstarch mixture until the mixture thickens.

Microwave chocolate pieces in a microwave-safe bowl for 1 minute, or until melted and smooth, stirring occasionally.

Pour half of the coconut mixture into a separate bowl and set aside.

Add the melted chocolate to the remaining coconut mixture in the saucepan and stir until well combined.

Pour the chocolate-coconut mixture into the baked pie crust, spreading evenly.

Carefully layer the reserved coconut mixture on top of the chocolate layer.

Cool the pie in the refrigerator for at least 1 hour to allow it to set.

In a mixer, whip heavy cream with 1/4 cup sugar until stiff peaks form.

Layer the whipped cream on top of the chilled pie.

Garnish the pie with shaved chocolate.