In a cocktail shaker, combine cranberry-cinnamon shrub, rum and lime juice.
Shake over ice and strain into a rocks glass.
Add fresh ice and top with club soda.
Add a cinnamon stick for garnish.
*Cranberry-Cinnamon Shrub: Place 1/2 cup fresh cranberries, 3 cinnamon sticks, 1/2 cup sugar and 1/2 cup water in a pot. Bring to a boil. Reduce heat to low and simmer for about 15 minutes. Let the mixture cool, strain out the cranberries and cinnamon sticks, and add 1/8 cup white rice vinegar. Stir and let settle in storage container. Refrigerate until ready to use.
A Note on Shrubs: Shrubs were popularized in 17th Century England, as vinegar was used as a method of preserving fruits. This practice was brought to colonial America, where vinegar-infused fruits mixtures were added with sweeteners to make a syrup that is both sweet and sour.