I have almost no reference point for egg nog. (Though, as always, one Simpsons quote: "'Tis the season, Marge! We only get thirty sweet noggy days. Then the government takes it away again.") I gather that it's like a drinkable custard with warm spices. Wikipedia tells me that it's also known as egg milk punch. Ummm, that sounds horrible.
This vegan nog isn't horrible at all - it's a soymilk-based cocktail, taken from my recipe calendar, that made for a nice weeknight dessert. I don't like drinking soymilk straight up but there's enough brandy here to distract me from any beany-ness. Though you could just stir the ingredients together, I'd highly recommend getting out a blender, stick blender or cocktail shaker for a frothy top.
(looks to be sourced from She Knows)
1 1/3 cups soy milk
1/4 teaspoon ground cloves
1/4 teaspoon ground nutmeg
1/2 teaspoon ground cinnamon
1/3 cup brandy
2 1/2 teaspoons maple syrup
Place all the ingredients in a blender and blend until frothy; serve over ice.