In a large mixing bowl, combine the eggnog, heavy cream, peppermint syrup, vanilla extract, ground nutmeg, and ground cinnamon. Whisk until well combined.
Gently fold in the chilled club soda to add a fizzy element to the punch.
Taste the mixture and adjust sweetness by adding more peppermint syrup if desired.
Refrigerate the punch for about 30 minutes to allow the flavors to meld together.
When ready to serve, pour the punch into glasses filled with ice.
Top each glass with a dollop of whipped cream and sprinkle crushed peppermint candies over the top for a festive touch.
Notes
Adjust sweetness by adding more peppermint syrup if desired.