Combine the sugar, water, cloves, cinnamon stick and ginger in a small saucepan. Bring to a boil over medium-high heat stirring to allow the sugar to dissolve. Lower the heat and simmer for 5 minutes.
Remove from heat and let cool to room temperature. About 15 minutes. Cover and refrigerate for up to 2 weeks.
For the Martinis
Combine liquid ingredients in a cocktail shaker filled with ice. Shake well.
Pour into two chilled martini glasses and top with a sprinkle of crumbled gingersnap cookies.