Heat 2-1/2 cups milk in a medium saucepan.
Split the vanilla bean lengthwise and scrape out the seeds; add the seeds and pod to the saucepan and simmer over medium heat.
In a large bowl, whisk the eggs, sugar and cornstarch until it turns light yellow.
Temper the eggs by gradually pouring the hot milk mixture, about 1 cup at a time, into the egg mixture, whisking constantly.
Pour the mixture back into the pan.
Place over medium heat and stir constantly with a wooden spoon until the eggnog begins to thicken, about 6-7 minutes.
Remove from the heat and immediately stir in the remaining 1/2 cup milk to stop the cooking.
Remove the vanilla pod, let it cool and transfer to a pitcher, chill until ready to serve.