Start by adding the rice and water to the pitcher of a blender. Blend for 1-2 minutes, or until the rice is broken down into small pieces.

Place the cinnamon stick into the pitcher, cover, and refrigerate the mixture for at least 4 hours, preferably overnight, to allow the flavors to meld.

After soaking, strain the rice mixture through a fine mesh sieve lined with cheesecloth, positioned over a clean pitcher, to extract the rice milk.

While the rice milk is straining, combine the pumpkin puree, coconut milk, and coconut sugar in a small saucepan. Cook over medium heat, whisking continuously, until the sugar is fully dissolved, about 3-4 minutes.

Remove the pumpkin mixture from the heat and stir in the vanilla extract.

Pour the pumpkin mixture into the strained rice milk, stirring until thoroughly combined.

To serve, prepare a glass by rimming it with cinnamon sugar. Fill the glass with ice and add 1 ½ ounces of spiced rum. Pour the pumpkin spice horchata over the rum and stir gently with a cinnamon stick.

Garnish with an extra cinnamon stick and enjoy immediately.