In a small skillet, toast the clove, allspice, white pepper, cinnamon, and nutmeg over medium heat until fragrant, about 2 minutes.
Transfer to a sealable quart jar with the ginger and pour in the vodka. Seal and steep for 2 days, shaking the jar every 12 hours.
After 2 days, strain out the solids and transfer them to a small saucepan with the sugar and water. Bring to simmer, and cook until the sugar dissolves, about 2 minutes. Let cool completely.
Strain the syrup into the jar with the infused vodka, and shake to combine.
Serve on the rocks, in a cup of coffee, or stirred into your favorite cocktails.