Defrost blueberries. Put 200 ml coconut milk and sugar in a blender. Peel and grate the ginger. Add blueberries and puree everything at the highest setting. Divide the remaining coconut milk into four glasses and carefully pour on the blueberry smoothie.
Stir briefly with a spoon to create a blue and white marbling. Garnish with coconut shavings as desired and serve immediately.