Put the instant coffee and hot water in a large bowl and stir until dissolved.
Add the granulated sugar. Whisk the mixture vigorously until it is light and airy and holds peaks like whipped cream. This can be with a whisk, a hand mixer, a stand mixer, or a frother.
Steam the milk in a frother or on the stovetop using a whisk until hot.
Put the chocolate shavings and half of the crushed candy canes into a cup. Add the peppermint syrup and pour the hot steamed milk over the top.
Top with whipped coffee, whipped cream, and crushed candy canes.