Put the milk, cinnamon sticks, cloves, and 1/2 tsp vanilla into a large saucepan. Put it over the lowest heat setting on your stove for 5 minutes.
In a separate bowl, whisk together the egg yolks and sugar for 1 minute.
Turn the heat under the milk up to medium-high heat. Remove the cinnamon sticks.
Slowly whisk in about 1/4 of the hot milk into the egg/sugar mixture. Then pour all of the egg/sugar mixture back into the saucepan and whisk it all together. Put it over medium heat, whisking constantly, for 3 minutes. It will thicken a bit.
Pour the hot eggnog into a large bowl or beverage container and let cool at room temperature for 1 hour. Add cinnamon sticks back in (optional).
After 1 hour, stir in the heavy cream, 2 teaspoons vanilla, and nutmeg. Store in the fridge and allow to cool for at least 4 hours before serving.
Video
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Notes
For an uncooked version, whisk egg yolks, sugar, cloves, and nutmeg in a large mixing bowl. Replace the cinnamon sticks with 1/2 teaspoon ground cinnamon and whisk in with the egg yolks. Slowly pour in milk, cream, and vanilla extract, whisk until thoroughly combined.
Alcohol can be added before serving, to taste. Dark rum, cognac, and bourbon are all traditional options.