Heat half-and-half, cinnamon sticks, and cloves in a saucepan, stirring, until boiling. Remove from heat and let stand for 1 hour. Strain and return to pan.
Whisk egg yolks and sweetened condensed milk into half-and-half. Cook, stirring constantly over medium heat, until mixture reaches 160° (don't boil). Stir in coconut milk. Let cool, then chill at least 3 hours and up to 3 days.
Buzz half of mixture at a time in a blender until frothy. Pour into a bowl and stir in rum if you like. Ladle into glasses and sprinkle with ground cinnamon.