Step 1: In a large, heat-proof bowl, whisk together the egg yolks and granulated sugar until the mixture is pale yellow and creamy. Continue whisking until the sugar has mostly dissolved.
Step 2: In a large saucepan, combine the whole milk, heavy cream, and salt. Heat over medium heat, stirring occasionally, until the mixture just begins to simmer around the edges (small bubbles forming) but is not boiling. Do not let it boil.
Step 3: While continuously whisking the egg yolk mixture, slowly pour about half of the hot milk mixture into the yolks. This process, known as tempering, gradually raises the temperature of the eggs without scrambling them. Once combined, pour the tempered egg mixture back into the saucepan with the remaining hot milk.
Step 4: Return the saucepan to medium-low heat. Cook, stirring constantly with a wooden spoon or heat-proof spatula, until the mixture thickens enough to coat the back of the spoon. This typically takes about 5-8 minutes. The temperature should reach 160-170°F (71-77°C) for safe consumption. Do NOT let it boil at any point during this step.
Step 5: Immediately remove the saucepan from the heat. Pour the cooked egg nog mixture through a fine-mesh sieve into a clean bowl. This step ensures a silky smooth texture by removing any small bits of cooked egg.
Step 6: Stir in the vanilla extract or vanilla bean paste. Cover the bowl tightly and chill thoroughly in the refrigerator for at least 4 hours, or preferably overnight, to allow the flavors to meld and the egg nog to thicken further.
Step 7: When ready to serve, whisk the chilled egg nog until smooth. Pour into individual glasses and garnish generously with freshly grated nutmeg. For an alcoholic version, stir in your preferred spirits (such as brandy, rum, or bourbon) to taste before serving.