Combine milk, cinnamon stick, peppercorns, and cloves in a saucepan over medium-low heat. Heat until almost boiling; add vanilla pudding mix, reduce heat to low, and boil, stirring constantly, about 5 minutes. Remove from heat and strain into a large bowl. Refrigerate for 2 hours.
Combine milk mixture, condensed milk, and rum in a blender; blend until well combined.