Make the coconut sauce: In a saucepan mix together the coconut milk and sugar. Heat until little bubbles start to appear. You just want it hot enough to melt the coconut milk and sugar. You don’t need to simmer it. Add the lime zest and remove from heat to cool to room temperature.

To make the strawberry sauce: In a blender jar or a tall canning jar with a stick blender, combine the strawberries and sugar. Blend until smooth, and set aside.

To make the shave ice: Add shaved ice to a cup, glass, or bowl. Drizzle the coconut sauce and strawberry sauce over top. Sprinkle with diced pineapple, and top with ice cream or a drizzle of sweetened condensed coconut milk. If desired, you can also top with whipped coconut cream. Eat right away.