Rinse rice multiple times and soak along with cinnamon stick in a bowl of water for 4-5 hours.
Drain the rice and cinnamon. Transfer to a blender. Blend along with 500 ml water to get smooth milk-like consistency.
Pass this mixture through a muslin lined sieve. Discard the coarse particles. This is the horchata.
To prepare pumpkin puree, pressure cook the cubed pumpkin for 2 minutes with 1/4 cup water. When cool, remove to a mixer and blend to a puree.
To prepare the pumpkin spice mix, combine cinnamon powder, ginger powder, grated nutmeg and cloves in a spice grinder. Grind to a fine powder. You can sieve this powder a couple of times to remove any lumps or larger particles.
To prepare the base mix, combine horchata, pumpkin puree and 1 tsp of pumpkin spice in a pan along with sugar and bring to a gentle simmer. Thin with water if required to get the consistency of milk. This can be refrigerated at this stage or used to prepare any hot or cold pumpkin-spice beverages.
To prepare a cup of the horchata pumpkin spice latte, combine 1/4 cup each of milk and 1/2 cup of the horchata mix and heat over a low flame, frothing it well with a coffee frother. Add a pinch of pumpkin spice to this and any extra sugar to your taste.
Take 1/4 cup or less of brewed coffee in a cup. Add the heated mixture in the pan to the coffee. Stir. Serve warm.