Brew your coffee and allow it to cool to room temperature. You can also brew it in advance and refrigerate it.
In a blender, combine the coconut milk, coconut syrup, and strawberry puree. Blend until smooth and well mixed.
Fill a glass with ice cubes, then pour in the cooled coffee until the glass is about halfway full.
Slowly pour the coconut-strawberry mixture over the coffee, allowing it to swirl and create a beautiful layered effect.
Garnish with shredded coconut and fresh strawberries if desired. Serve immediately.