Step 1: In a medium bowl, whisk together the egg yolks and sugar until light and creamy. Set aside.
Step 2: In a heavy-bottomed saucepan, combine the whole milk, heavy cream, ground cinnamon, ground nutmeg, and ground cloves. Heat over medium-low heat until the mixture is hot and just barely simmering, but not boiling. Stir occasionally to prevent scorching.
Step 3: Slowly ladle about 1/2 cup of the hot milk mixture into the egg yolk mixture, whisking constantly. This is called tempering and prevents the eggs from scrambling. Repeat with another 1/2 cup of hot milk mixture.
Step 4: Gradually pour the tempered egg yolk mixture back into the saucepan with the remaining hot milk, whisking continuously. Continue to cook over medium-low heat, stirring constantly with a wooden spoon or spatula, until the eggnog thickens enough to coat the back of the spoon (this usually takes 5-10 minutes). Do not let it boil.
Step 5: Remove the saucepan from the heat. Add the semi-sweet or dark chocolate chips and stir until the chocolate is completely melted and smooth. The residual heat will melt the chocolate.
Step 6: Stir in the vanilla extract and, if using, the rum or bourbon. Taste and adjust sweetness or spices if desired.
Step 7: Pour the chocolate eggnog into a heatproof pitcher or container. Cover and refrigerate for at least 4 hours, or preferably overnight, to allow the flavors to meld and for the eggnog to chill thoroughly.
Step 8: To serve, pour the chilled chocolate eggnog into glasses. Garnish with whipped cream or marshmallows, chocolate shavings or cocoa powder, a sprinkle of fresh nutmeg, or a mini candy cane for a festive touch.