Place an 8-inch square baking dish in the freezer to chill while you make the simple syrup.

Combine the sugar and 1/2 cup of water in a small saucepan over low heat until the sugar is dissolved and syrup is at a gentle boil. Remove it from the heat, and allow it to cool. Cook's Note: I like to pour the syrup into a shallow bowl so that it cools more quickly.

Pull the chilled baking dish out of the freezer, and pour the coconut milk into the dish. You may need to whisk it to smooth out any lumps.

Whisk in the simple syrup, lime zest, lime juice and fresh coconut until well combined. Place the dish in the freezer, and let it chill for 1 hour.

Pull it out of the freezer, and using a fork, break up the ice crystals forming around the edge of the dish, by dragging them into the more molten center. Return to the freezer and repeat this process every hour or so, smoothing out the granita before you return it to the freezer. The whole process should take about 3 hours. When you're ready to serve, allow the granita to sit at room temperature for about 5 minutes so that it softens. Spoon the mixture into a small bowl or glass, and top with a little coarse sea salt