Stir the instant coffee and sugar into ½ cup warm water until dissolved. Add the cold milk and stir. Let the mixture cool before pouring it over the ice cubes.

Place your desired number of eggnog ice cubes in a large glass. Pour the cooled coffee mixture over them.

In a separate container, froth the remaining ½ cup eggnog with a handheld milk frother. Alternatively, shake cold eggnog in a tightly sealed jar until foamy.

Pour the frothed eggnog over the coffee and sprinkle with cinnamon, if desired. Add a splash of extra milk or eggnog to suit your taste.