In a large bowl, whisk together the egg yolks and granulated sugar until smooth and slightly thickened.
6 egg yolks, ½ cup granulated sugar
In a medium saucepan, combine the whole milk, whipping cream, cinnamon sticks, and a pinch of salt. Stir well.
2 cups milk, 1 cup whipping cream, 2 cinnamon sticks, ¼ teaspoon salt
Warm the mixture over medium heat until it is just below a low boil. Turn off the heat and let it cool for five minutes.
Slowly drizzle the hot milk mixture into the egg mixture while whisking constantly so the hot liquid does not scramble the yolks.
Pour the combined mixture back into the saucepan. Cook over medium heat until the eggnog reaches 160°F. Use a candy thermometer or instant-read thermometer to check the temperature.
Once the mixture thickens slightly and coats the back of a spoon, remove it from the heat, add the vanilla extract and let it cool completely.
½ vanilla extract
Strain the eggnog through a fine-mesh sieve into a bottle or an airtight container, then refrigerate until chilled.