Combine all ingredients in except for whole cranberries in an ice-filled cocktail shaker. Shake vigorously for 20 seconds. Double strain into chilled coupe glass. Garnish with cocktail skewer of fresh cranberries.
Cut ½ cup of cranberries in half; set aside.
Combine remaining cranberries, red wine, sugar, cinnamon, apple and ginger in a medium saucepan over medium heat.
Bring to a low boil, stirring frequently. Adjusting heat as needed, briskly simmer mixture, uncovered, for 15 minutes. Stir in reserved cranberry halves; simmer another 5 minutes. Cool, cover and refrigerate until needed. (Compote can be made 2 to 3 days ahead.)