Whisk together first 3 ingredients in a large heavy saucepan. Gradually whisk in milk, coconut milk, and cream. Cook over medium heat, stirring constantly, 10 to 12 minutes or until mixture thickens slightly. Remove from heat.
Whisk egg yolk until slightly thickened. Gradually whisk about 1 cup hot cream mixture into yolk. Add yolk mixture to remaining cream mixture, whisking constantly. Whisk in vanilla bean paste. Cool 1 hour, stirring occasionally.
Place plastic wrap directly on cream mixture, and chill 8 to 24 hours.
Stir in toasted coconut. Pour mixture into freezer container of a 1 1/2-qt. electric ice-cream maker, and freeze according to manufacturer's instructions. (Instructions and time may vary.)