Make sure your coconut milk is cold and firm. Scoop only the thick bits out of the can (if you chose a full fat coconut milk, this should be the majority of the contents). Divide the thick coconut milk into two portions; reserve the remaining liquid for another use.
Blend half of the coconut milk with the strawberries and sweeten with 1 teaspoon of xylitol. Whip the other half of the coconut milk with the vanilla and remaining xylitol.
Spoon the strawberry mixture into serving glasses, then top with the cream mixture. Chill till serving.
If you use Stevia as the sweetener, use half the amount.