In bowl of blender, add evaporated milk, cream of coconut, coconut milk, sweetened condensed milk, rum (if using), vanilla extract, ground cinnamon, and nutmeg. Blend on high until mixture is well combined, 1-2 minutes.

Pour coconut mixture into 2 one quart glass air tight sealable containers, add one cinnamon stick to each if desired. Transfer to refrigerator. Chill until cold. Best results if you let sit overnight in fridge before serving.

To serve, stir or shake well to combine. Pour into small serving glasses. Garnish with ground cinnamon and cinnamon sticks, if desired.