In a heavy-bottomed 3-quart saucepan, combine cream, half-and-half, and sugar. Bring to a simmer over medium heat; do not boil.
In a medium bowl, combine egg yolks and coconut extract. Add 2 cups hot cream mixture to egg mixture. Return to medium heat, and cook for 6 to 7 minutes or until mixture coats the back of a spoon. Remove from heat, and let cool for 10 minutes.
Strain mixture through a fine-mesh strainer into an airtight container. Stir in mango puree. Cover, and refrigerate for 4 hours to overnight. Pour mixture into an ice-cream freezer, and freeze according to manufacturer’s instructions. Ice cream will be soft. For firmer ice cream, place in an airtight container, and freeze for several hours to overnight.