If you want to decorate the glasses with grated chocolate, do it before making and adding the cocktail to the glass.
To decorate the glass: dip the rim of the glass into soft ice cream, chocolate syrup, or melted chocolate and then into the grated chocolate. (To make grated chocolate, you can use a fine cheese grater to grate a chocolate bar.)
Combine ice cream, ice, Crème de menthe, Crème de cocoa, and vodka in a blender and blend until completely smooth.
Divide the mixture between two glasses and garnish with some whipped cream and grated chocolate.
Video
Notes
Want to make it non-alcoholic? Use the same vanilla ice cream and in addition to ice cream, add about 1/2 cups of milk, 1 cup of ice, 2-3 tablespoons of crème de menthe syrup (non-alcoholic and can be found in coffee syrups isle and mixers isle of the grocery store), and either a couple of tablespoons of chocolate syrup or a couple of ounces of a chocolate bar. Blend it all and serve.
Lactose or dairy free: you can simply use lactose free or dairy free vanilla ice cream to make this drink. For whipped cream, you can use dairy free option available at the grocery store, like once made with coconut milk or oat milk.