In a saucepan, combine cinnamon sticks, evaporated milk and coconut milk.
On a medium low heat, bring it to a light simmer, stirring frequently so that the milk does not scorch. DO NOT BOIL.
Keep on low heat and let it simmer for 5 minutes.
Remove from heat, cover and let it rest at least 1 hour or overnight in the refrigerator.
Discard the cinnamon sticks.
In a high powered blender, combine the steeped milk with the cream of coconut, sweetened condensed milk and pumpkin.
Add vanilla extract, almond essence and pumpkin spice.
Blend well until thoroughly combined.
Add rum and mix again until well incorporated.
Using a funnel, transfer into glass bottles.
Chill for at least 4 hours in the refrigerator.
Serve as is or over ice.
If desired, rim the serving glass with the wedge of a lime.
Rim the glass with grated coconut.
Pour coquito to fill the glass.
Garnish with freshly grated nutmeg or more pumpkin spice.