In a dry skillet over medium-low heat, add the almonds, coconut flakes, and broken cinnamon sticks. Lightly toast just until the almonds start to turn golden brown and fragrant, about 4 to 5 minutes, stirring occasionally to make sure the almonds don’t burn. We don’t want to completely toast them or they’ll overpower the flavor. Remove from heat.
In a large bowl, mix together the rice, coconut flakes and cinnamon sticks, then pour in the hot water. Set aside and let rest for 4 to 6 hours. Make sure the water is hot to the touch but isn’t boiling. We don’t want to cook the rice.
Pour the mixture (liquid and all) into a blender, and blend for 30 seconds, then strain through a fine-mesh coffee filter (to ensure your horchata isn’t chalky or grainy) into a pitcher. Stir in the cold water and vanilla extract, then let chill for 2 hours in the refrigerator.
Once you’re ready to serve, whisk in the coconut milk and sweetened condensed coconut milk (this is to prevent any coconut fat from solidifying in the refrigerator). Serve over ice, garnished with toasted coconut.
Note: You can find sweetened condensed coconut milk at Whole Foods and Walmart, and on Amazon.