Cook and stir shredded coconut in a skillet over medium-low until lightly browned and fragrant, about 5 minutes.
Combine coconut milk, sugar, and toasted coconut in the top of a double boiler over simmering water; simmer until slightly reduced, about 1 hour. Pour coconut milk mixture through a strainer and pour liquid back into double boiler.
Fill a large bowl with ice water.
Whisk egg yolks into coconut milk mixture until thickened. Remove double boiler from heat and place the top portion in the ice water to cool the coconut milk mixture to room temperature, about 20 minutes.
Process coconut milk mixture in an ice cream maker according to manufacturer's instructions.
This recipe contains raw eggs. We recommend that pregnant women, young children, the elderly, and the infirm do not consume raw eggs. Learn more about egg safety from our article, Making Your Eggs Safe.