Muddle cranberries, add remaining ingredients with ice. Shake, double strain, chilled cocktail glass, garnish.
To make ginger syrup bring 1 cup water and 1 cup Demerara sugar to a boil. Reduce heat to a simmer, stir till sugar is dissolved, about 3 minutes. Remove from heat and cool. Place in blender with 1 cup diced ginger, purée. Fine strain and store for up to two weeks.
The American Cocktail, by the Editors of Imbibe Magazine