Place all ingredients except vanilla into large pot. Let sit for five minutes. Turn heat to medium-high, stirring occasionally, until pudding starts to boil. Continue stirring until the boiling continues even as you stir.
Remove pan from heat, stir in vanilla, and let cool.
Coconut: Although classified by the FDA as a tree nut, coconut is not a common allergen and is not related to tree nuts. If you have a tree nut allergy, consult your physician to find out if you need to avoid coconut.
Egg Substitutions: There are many egg-free products and foods available to make your recipes free of eggs. Find out more about egg substitutions.