For the syrup: In a small saucepan, combine the water, sugar, ginger, cinnamon, and cloves over medium heat. Bring to a boil, reduce the heat and simmer for 5 minutes, stirring occasionally, until the sugar has dissolved. Take the pan off the heat and allow the syrup to cool, about 20 minutes. Remove the ginger, cinnamon, and cloves and discard.
For the espresso: In a 1-cup glass measuring cup, whisk together the boiling water, espresso powder, and liqueur, if using, until the powder is dissolved.
Scoop the gelato into 4 dessert bowls or glasses. Pour 1/4 cup of the syrup and 2 tablespoons espresso over each. Serve immediately.