Chill the coconut milk in the fridge overnight. Open the can and scoop the thick part of the coconut milk from the top of the can into a large bowl.
Use an electric mixer to whip the coconut milk and peanut butter until light and smooth, about 1-2 minutes. Add the remaining ingredients and continue whipping until fluffy and a mousse-like consistency, another 1-2 minutes.
Spoon into two serving containers and refrigerator for 30-60 minutes. Top with dairy free whipped cream, strawberries, and shaved chocolate if desired.