Combine the first 3 ingredients in a medium, heavy saucepan, and bring to a boil. Remove milk mixture from heat.
Combine sugar and egg yolks; beat with a mixer at high speed until thick and pale. Gradually add half of hot milk mixture to sugar mixture, stirring constantly with a whisk. Return milk mixture to pan. Cook over medium-low heat 2 minutes or until a thermometer registers 160°, stirring constantly. Place pan in a large ice-filled bowl. Cool completely, stirring occasionally.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Stir in coconut and cookies. Spoon ice cream into a freezer-safe container; cover and freeze 1 hour or until firm.