In a medium saucepan, combine the coconut milk, cream and sugar. Heat and stir until the sugar is completely dissolved. Allow the mixture to cool completely, then refrigerate for at least 1 hour before churning.
Add the mixture to your ice cream maker according to manufacturer’s instructions. Mix until you reach the desired consistency. Add the freshly grated coconut once the mixture thickens and is ready to be transferred to a freezer container.
Freeze until ready to serve, at least 1 hour. Garnish with toasted coconut upon serving.
To toast coconut:
In a small skillet over low heat, melt a small amount of butter (about a teaspoon per cup of grated coconut). Once melted, add coconut and stir to coat. Allow to toast (be patient), stirring occasionally. Be extremely careful not to burn the coconut. Once toasted, spread out on paper towels to cool. Store in an airtight container until ready to use.