Combine 1 1/2 cups milk, cinnamon sticks, vanilla bean, cloves, peppercorns, ginger, cardamom pods, and salt in a saucepan.

Bring to a simmer over medium heat.

Turn off heat and let stand for 15 minutes to infuse flavors.

Strain the mixture through a sieve, discarding solids except the vanilla bean.

Scrape the vanilla bean seeds into the milk; discard the pod.

Return the infused milk to the saucepan over medium heat.

In a bowl, beat eggs and sugar until light and lemon colored (about 2 minutes).

Gradually whisk in the heated milk into the egg mixture.

Return the egg-milk mixture to the saucepan.

Cook over medium heat, stirring constantly with a wooden spoon, until it thickens and coats the back of the spoon (4-6 minutes).

Do not simmer or boil to prevent scrambling.

Add the remaining 1/2 cup of cold milk to stop the cooking process.

Transfer the mixture to a pitcher.

Chill for at least 2 hours or until very cold.

Divide the eggnog among four chilled glasses.

Stir in brandy or rum (optional).

Garnish with freshly grated nutmeg.