Bring whole milk and cinnamon stick to a simmer in a medium saucepan over medium heat. Remove from heat, and transfer to a bowl. Whisk in condensed milk, flour, and vanilla. Refrigerate for at least 30 minutes.Advertisement
Strain mixture through a fine sieve, and stir in rum if using. Divide among 4 ice-filled glasses. Garnish with ground cinnamon and cinnamon sticks.
Strained horchata can be refrigerated for up to 3 days.