Combine coconut milk, evaporated milk and sweetened condensed milk in large saucepan set over medium heat; bring to a simmer.
Meanwhile, beat egg yolks with electric mixer until thick and pale yellow. Gradually whisk in half the hot milk mixture into egg yolk mixture. Pour into saucepan. Reduce heat to medium-low. Cook, stirring constantly with wooden spoon or spatula, for 5 to 8 minutes or until mixture thickens and coats back of spoon.
Remove from heat. Strain through fine-meshed sieve and cool completely. Stir in rum, brandy and vanilla. Cover and chill in refrigerator for at least 6 to 8 hours and up to 3 to 5 days.
Whipped coconut cream: beat hardened cream of coconut, heavy cream, powdered sugar and vanilla in chilled mixing bowl with electric mixer on high speed for 2 to 3 minutes or until creamy, light and fluffy. Chill until ready to use.
Fold whipped coconut cream into eggnog and divide into 6 glasses. Garnish each with pinch of nutmeg.
Optional: If rimming glass, place agave into shallow dish and crushed cookies in another dish. Wet rims of glasses with agave mixture and then dip in cookies. Let stand for 10 minutes.
Substitute nutmeg with ground cinnamon or for festive addition, use gingerbread or pumpkin pie spice.