Rub one lemon half around the rim of each of four glasses, then dip the rims into the cinnamon sugar to coat evenly.
Add the pumpkin puree, maple syrup, pumpkin pie spice, and remaining lemon juice to a cocktail shaker.
Pour in the vodka, fill the shaker with ice, and shake hard for 15 seconds until the mixture is well chilled.
Fill the prepared glasses with fresh ice, then strain the drink into each glass.
Place one cinnamon stick in each glass for garnish.