1. Whisk together evaporated milk and dry milk in a 4-qt. slow cooker until smooth. Whisk in milk and next 2 ingredients. Add chocolate morsels. Cover and cook on Low 4 hours, whisking until smooth after 2 hours.
2. Preheat broiler with oven rack 3 inches from heat. Place 12 marshmallows on a parchment paper-lined baking sheet. Broil 2 minutes or just until toasted. Repeat procedure with desired amount of marshmallows. Stir vanilla into hot chocolate, and ladle into mugs. Stir 1 tablespoon liqueur into each serving, if desired, and top each serving with 1 to 2 toasted marshmallows.