Combine the instant coffee granules, granulated sugar, and very hot water in a bowl. Whip with a hand mixer for approximately 2–4 minutes, until the mixture is thick, glossy, lighter in color, and able to hold soft peaks. A balloon whisk may be used, but it usually takes 5–8 minutes.

For the nonalcoholic version, fill two glasses with ice and divide the cold milk between them. Spoon half of the whipped coffee over each glass, then stir before drinking because the coffee foam is intentionally very concentrated.

For each cocktail, fill a glass with ice and add 1½ ounces of coffee liqueur plus 1 ounce of vodka, if using. Add approximately ¾ to 1 cup milk or cream to each glass, leaving room for the topping, then spoon half of the whipped coffee over each drink.

Serve both versions immediately while the foam is thick and airy. Stir just before serving so the concentrated coffee topping blends into the cold milk or cocktail.