In a 16-ounce or larger jar with a lid or resealable container, combine granulated sugar and water. Using a microplane or fine grater, grate ginger into jar. Cover and shake jar until sugar has dissolved, 3 to 4 minutes.
Using a fine-mesh sieve, strain ginger mixture into a small bowl, pressing with the back of a spoon to expel as much liquid as possible. Discard solids.
Make Ahead: Ginger simple syrup can be made 3 weeks ahead. Store in an airtight container and refrigerate.
In a cocktail shaker, combine bourbon, ginger syrup, and cranberry juice. Fill shaker with ice and vigorously shake until outside of shaker is very frosty, about 20 seconds.
Strain into a rocks glass or coupe. Garnish glass with orange peel.
