In a large bowl, beat the egg yolks with an electric mixer or a whisk until they become light and creamy. Gradually add 1/2 cup of sugar, and continue to beat until the sugar is dissolved.
Slowly whisk in the milk, heavy cream, and the chosen alcohol (bourbon, rum, or brandy), followed by the nutmeg, cinnamon (if using), and vanilla extract. Mix until well combined.
In a separate bowl, beat the egg whites until soft peaks form. Gradually add the remaining 1/4 cup of sugar, and continue to beat until stiff peaks form.
Gently fold the egg whites into the egg yolk mixture until fully incorporated.
Chill the eggnog in the refrigerator for at least 2 hours or preferably overnight, allowing the flavors to meld together.
Before serving, give the eggnog a good stir to ensure even distribution of ingredients. Serve in cups or glasses, garnishing with a sprinkle of nutmeg or cinnamon on top, if desired.
Notes
Note: Consuming raw eggs carries a risk of foodborne illness, especially for people with weakened immune systems, pregnant women, and young children. To reduce the risk, you can use pasteurized eggs or make a cooked eggnog base by heating the milk and egg mixture until it reaches 160°F (71°C), then cooling it before proceeding with the recipe.