Combine 1 cup water and the granulated sugar in a saucepan and cook over medium-high heat, stirring until the sugar dissolves.
Add the cinnamon stick and orange zest and let the mixture sit until the flavors infuse, about 5 minutes.
Discard the cinnamon stick.
Add the instant coffee and stir until completely dissolved. Keep aside to cool.
Blend the syrup and ice cream in a blender until smooth.
Whip the cream and add the powdered sugar and continue to whip to stiff peaks. Add a dollop of whipped cream over each glass of shake and dust with ground cinnamon.
Serve (immediately, or keep in the freezer until required).