Step 1: In a large heatproof bowl, whisk together the egg yolks and granulated sugar until the mixture is pale yellow and thick. Set aside.
Step 2: In a medium saucepan, combine the whole milk, heavy cream, and salt. Heat over medium-low heat, stirring occasionally, until the mixture is hot and just barely simmering around the edges. Do not let it come to a rolling boil.
Step 3: Slowly, while continuously whisking, ladle about half a cup of the hot milk mixture into the egg yolk mixture. Continue to whisk constantly. Gradually add another half cup, then another, until the egg mixture is warmed (tempered). This prevents the eggs from scrambling.
Step 4: Once tempered, slowly pour the warmed egg mixture back into the saucepan with the remaining hot milk, whisking constantly. Continue to cook over medium-low heat, stirring frequently with a wooden spoon or spatula, until the eggnog thickens enough to coat the back of the spoon (reaching approximately 160°F or 71°C). Do not boil.
Step 5: Remove the saucepan from the heat immediately. Stir in the pure vanilla extract. For an extra smooth consistency, pour the homemade eggnog through a fine-mesh sieve into a clean bowl or pitcher.
Step 6: Cover the eggnog and refrigerate for at least 3 hours, or preferably overnight, to allow the flavors to meld and the mixture to thoroughly chill and thicken.
Step 7: Before serving, give the homemade eggnog a good whisk. If adding alcohol, stir it in now. Pour into festive glasses and garnish with freshly grated nutmeg and a cinnamon stick. Enjoy your rich and creamy homemade eggnog!