Fill the glass bottles with very hot water and allow them to sterilize for about 10-15 minutes. Empty the bottles and add a cinnamon stick to each bottle. Set aside.
Place a small pot over high heat. Add 1 cup of water and the cinnamon sticks, cloves, star anise, allspice, nutmeg. A small piece of fresh ginger is optional. Bring this to a boil and steep for about 10 minutes. If you prefer a strong spice taste, steep for longer.
To a blender, add the coconut milk, cream of coconut, evaporated milk, condensed milk, ½ cup of the spiced tea, almond extract, and rum. Blend for 1 minute on low speed until smooth.
Add the pumpkin puree and pumpkin spice. Blend again until smooth.
Pour the coquito into the glass bottles using a funnel. You can also use a strainer if you prefer, for a smoother texture. Leave a 1-inch space at the top of each bottle to allow room for shaking later.
Store in the refrigerator for up to 4 weeks. The coquito will thicken over time. Shake vigorously before serving.
Serve chilled coquito in a glass rimmed with ground cinnamon, a cinnamon stick and a sprinkle of nutmeg or cinnamon on top. Enjoy! ¡Buen provecho!
