Place the coconut milk and sugar in a medium-size, heavy-bottomed saucepan over medium heat. Bring the the mixture to a boil while stirring occasionally until the sugar fully dissolves, and continue to boil for about 1 minute. Remove from the heat and set aside to cool, at least 1 hour.
Pour into a clean container, cover with a lid or plastic wrap, and chill in the refrigerator for at least 8 hours or overnight.
When ready, pour the chilled mixture into the ice-cream maker and process according to manufacturer's specifications. When the sorbet is about 5 minutes from being done, slowly add the fresh zest. Finish processing the sorbet.
Remove the finished sorbet from the ice-cream maker and place in plastic container. Cover with plastic wrap by pressing the wrap gently against the top of the sorbet, affix lid to container, and place int the freezer to fully harden before serving.
Yield: approximately 1-1/2 quarts