Place the ice cream and half & half in the blender and pulse 5-6 seconds to blend. Add the hot cocoa mix, creme de cacao, vodka, and peppermint schnapps, and blend until smooth. Pour into a martini glass and garnish with whipped cream, chocolate curls, and candy canes.
Notes
To make a cinnamon boozy frozen hot chocolate cocktail, substitute the white cacao for dark chocolate cacao and the peppermint schnapps for cinnamon schnapps.