Toast ¼ cup of the sweetened coconut in a dry frying pan, until golden brown.
Heat the milk, coconut milk, heavy cream and remaining cup of shredded coconut until bubbles form around the edges of the pot.
While the milks are heating beat the egg yolks and sugar until pale yellow.
Once the milks have formed a line of bubbles around the inside edge of the pot remove it from the heat and strain the shredded coconut out. Discard the coconut.
Temper the egg yolks by drizzling ¼ cup of the hot milk mixture into the yolks while whisking. Repeat with another ¼ cup of hot milk mixture. Now it is safe to pour the remaining hot milk mixture into the bowl of yolks with out the yolks cooking.
Whisk for about 1 minute and strain through a fine mesh strainer into the pot you cooked the milks and whipping cream in.
Return the pot to the heat and cook the custard base until it thickens enough to coat the back of a spoon. Test for doneness by running your finger through the custard. If a trail remains your custard is done. If not continue cooking and check again after 5 minutes.
When your custard is done remove the pot from the heat and pour the custard into a bowl, preferably one with a pouring spout. If using an ice cream maker it will make pouring the ice cream base into it much easier.
Allow your ice cream base to cool on the counter to room temperature. Once cool cover with plastic wrap and chill in the refrigerator for at least 1 - 2 hours.
When the ice cream base has chilled completely churn in an ice cream maker per manufactures instructions.
Five minutes before your ice cream is finished add the ¼ of toasted coconut and continue churning.
Place ice cream in an airtight container and freeze overnight.
Makes about 4 ½ cup servings.