In a small saucepan, combine water and sugar over medium heat. Bring to a boil and reduce heat to low. Add the allspice, cinnamon, and ginger to the simple syrup and simmer for 5 minutes. Take pan off heat and set aside. To the 1 cup of brewed espresso, add 1 cup of boiling water. Pour 1/2 cup of espresso into each of 4 (6 to 8-ounce) serving cups. Add 2 tablespoons of the spiced simple syrup to each cup and stir to combine. In a large bowl, using an electric mixer with a whisk attachment, beat the heavy cream until soft peaks form. Add the confectioners' sugar and continue to beat until stiff. Top each cup of espresso with a dollop of whipped cream. Dust with cinnamon and serve.