*Make sure that you chill your coconut milk cans overnight or longer (without shaking them or moving them) so that the thick coconut cream completely separates from the watery coconut liquid. If the liquid mixes with the coconut cream, your final cream will be watery and will not whip well.
I've found that coconut milk cans are not always consistent - sometimes you get a dud can where the cream won't separate from the water. I usually buy an extra can just in case. For this recipe, I used Whole Foods' full-fat coconut milk, with success.
Note: My strawberries were more tart than sweet, so I sprinkled them with a little cane sugar and a pinch of salt to bring out more of their sweetness.