Place ice cream in an extra-large punch bowl. Add half the eggnog. Stir and mash mixture using a potato masher until ice cream is melted and mixture is well combined. Stir in remaining eggnog. Slowly pour in cream soda, stirring to combine. To each glass add a peppermint stick, cinnamon stick, or candy cane. Sprinkle lightly with cinnamon (about ⅛ teaspoon per serving). Makes about 24 (6-ounce) servings.