Step 1: In a medium bowl, whisk together the egg yolks and 1/2 cup granulated sugar until the mixture is light yellow and creamy.
Step 2: In a medium saucepan, combine the whole milk, heavy cream, the remaining 2 tablespoons sugar, and a pinch of salt. Heat over medium heat, stirring occasionally, until just simmering and small bubbles form around the edges (do not bring to a rolling boil).
Step 3: Slowly temper the egg yolk mixture: Ladle about 1/2 cup of the hot milk mixture into the egg yolks while continuously whisking vigorously to prevent scrambling. Repeat with another 1/2 cup of hot milk mixture.
Step 4: Return the tempered mixture to the saucepan. Cook over low to medium-low heat, stirring constantly, until an instant-read thermometer registers 160°F (71°C). Do not boil.
Step 5: Remove from heat and stir in the vanilla extract and 1/2 teaspoon freshly grated nutmeg.
Step 6: Pour the eggnog through a fine-mesh sieve into a clean bowl or pitcher to remove any small bits of cooked egg or spices. Cover tightly with plastic wrap directly on the surface of the eggnog to prevent a skin from forming, and chill in the refrigerator for at least 4 hours, or preferably overnight, to allow the flavors to meld and for the eggnog to thicken further.
Step 7: If using alcohol, stir it into the chilled eggnog just before serving.
Step 8: Serve the homemade eggnog cold, garnished generously with additional freshly grated nutmeg and optionally a cinnamon stick.