Separate the eggs into yolks and whites, reserving three egg whites. Beat the egg yolks until they're smooth and slightly lightened in color. Set aside.
Bring milk, heavy cream, maple syrup, cinnamon sticks, vanilla extract, nutmeg, whole cloves and pinch of salt to a simmer over medium heat. After the mixture comes to a simmer, turn off the heat.
Strain some of the cream mixture through a fine-mesh sieve into the egg yolks and whisk. Repeat this process until all of the milk mixture is incorporated.
Stir in Baileys. Cover and refrigerate overnight or up to three days before serving at your holiday gathering.
For an optional frothy topping, whip the reserved egg whites until soft peaks form immediately before serving and use to top each glass. Sprinkle with ground cinnamon and nutmeg if desired. Enjoy!