In a large bowl, beat egg yolks until light in color. Gradually add sugar and continue beating until well combined.
In a saucepan over medium heat, combine milk, heavy cream, cinnamon stick, and whole cloves. Heat until it just begins to simmer. Remove from heat, cover, and let it steep for about 20-30 minutes to infuse the flavors.
Strain the infused milk mixture to remove the cinnamon stick and cloves.
Slowly whisk the spiced milk into the egg yolk mixture, a little at a time, to temper the eggs.
Pour the entire mixture back into the saucepan and cook over low heat, stirring constantly, until it thickens enough to coat the back of a spoon. Avoid boiling.
Remove from heat and let it cool. Stir in bourbon, rum, vanilla extract, and ground nutmeg.
In a clean, dry bowl, beat the egg whites until stiff peaks form. Gently fold the egg whites into the eggnog mixture.
Refrigerate the eggnog for at least 4 hours or overnight to allow the flavors to meld.
Before serving, give it a gentle stir, and sprinkle with a little extra ground nutmeg on top.