In a large saucepan on low heat, whisk the coconut milk and maple syrup until warm. In a medium heat proof bowl mix the sugar and strawberry puree and mix until smooth, then whisk in the egg yolks. Pour mixture back into saucepan and cook the custard over low-medium heat whisking constantly for about 6 minutes until very hot and thickened. Do not let it boil.
Remove from heat and put in a glass container. Let cool.
If not using an ice cream maker- cover container and place in the freezer. Stir about every ½ hour for 2 hours. Then freeze an additional 4-6 hours (6-8 total), until firm.
If using an ice cream maker- skip Step 3. Freeze the ice cream in an ice cream maker according to the manufacturers' directions. Transfer to a glass or plastic container and freeze until firm, about 4 hours.
When ready to serve let set for about 5 minutes until soft enough to handle. Garnish with unsweetened coconut flakes or nuts.