In a blender, combine the pumpkin puree, coconut milk, cream of coconut, sweetened condensed milk, evaporated milk, rum, vanilla extract and pumpkin pie spice.
Blend on high speed just until combined. This took me about 2 minutes, but this will vary depending on the blender you own.
Refrigerate for 4 hours or overnight for best results.
Before serving, give the pumpkin coquito a quick shake as some of the ingredients may have settled to the bottom of the pitcher.
Finally, sprinkle with a little extra pumpkin spice if you wish and serve.