Refrigerate the unopened can of coconut milk overnight.
For best results, and cool, creamy whipped cream, place a small mixing bowl in the freezer for 20 - 30 minutes before you begin to make the whipped cream.
Open the can of coconut milk, being careful not to shake it!. The coconut cream solids will be at the top of the can. Scoop out the coconut solids into your chilled mixing bowl.
Add the maple syrup and beat the mixture with a hand mixer - start on low speed to break up the coconut milk solids and incorporate the syrup. Then turn to high speed until soft peaks form - about 3-5 minutes.
Add 2 tablespoons of the strawberry puree and mix into the whipped cream on medium speed until it is blended - about 1 minute. You can add the additional puree based on your taste. Depending on how much coconut solid you were able to get from your can, you can add all of the puree without making the whipped cream runny.
Add additional maple syrup as needed to sweeten to taste. Save the remaining coconut milk liquid for another use - like a smoothie!
Store the whipped coconut cream covered with plastic wrap or Tupperware in the refrigerator for up to 1 week.