Combine all ingredients in a cocktail shaker. Shake vigoroursly, then strain into a martini glass. Garnish as desired.
To make the ginger simple syrup, In a small pot bring the water and sugar to a boil. When boiling, add the ginger and reduce heat to a simmer for 45 minutes.
Place a colander over a bowl and drain the syrup. Discard the ginger.
Notes
If you decide to go the stirred route, combine all of your ingredients and ice in a mixing glass. Stir for 30 seconds and then strain into the glass.