Combine all of the ingredients (except star anise) in the blender or Vitamix. Blend on medium for 1 to 2 minutes until smooth. If the cream of coconut you’re using has a layer of coconut cream on the top (see Notes), you may need to mix it longer.
Transfer the mixture to a glass jar or bottle (see Notes) and add 2 whole star anise. You need something with a lid to keep it air-tight and also allow for shaking before serving.
Refrigerate for a minimum of 4 hours (see Notes) until completely chilled throughout.
Shake well before serving. Spices likely will settle on the top.
Fill an old fashioned or stemless wine glass with ice. Pour over ice and garnish with a sprinkle of cinnamon or nutmeg.
Notes
Cream of coconut is sweetened with sugar. Do not substitute coconut milk or light coconut milk – neither of these are sweetened. There may be a thick layer of coconut cream on the top when you open the can. If so, pierce it with a knife to break it. Use both the coconut cream and coconut milk (what’s below) for this recipe. Popular brands include Goya (15 ounces), Coco Reàl (21 ounces) and Coco Lopez (15 ounces). You will find them in the Mexican food section and/or liquor mixers section of your grocery store.
The prefered rum is a white (also called silver, clear or light) rum. Try Don Q which was recommended to me by our friend Antonio V who is a Coquito expert. I have also used Bacardi gold rum (but think the white rum is better).
I use a half gallon (8 cups) mason jar for each batch. You can also split one batch between two 25 ounce flip top bottles.
I make this 1 or 2 weeks in advance to allow the flavors to marinate. It keeps, chilled, for up to 6 months.