This easy homemade vanilla pudding recipe is wonderful served on its own, as a custard topping for waffles or crêpes, or as a delicious pastry cream for profiteroles, donuts, and eclairs.
In a medium, heavy bottomed saucepan, melt the butter and remove from heat. Stir in the flour, sugar, and salt (I like to mix them together ahead of time), and stir to combine. Add about 1 to 1-1/2 cups of the milk and stir until the mixture makes a smooth paste; then add the rest of the milk and stir to combine.
Return to medium heat and whisk until the mixture is hot and starts steaming. Beat the egg until frothy, and add to the hot milk mixture, stirring all the while. Continue whisking until the mixture begins to thicken. Whisk a couple minutes longer to cook through, remove from the heat, and stir in the vanilla.
Once the mixture is done, pour it into a glass bowl, cover it with plastic*, and refrigerate overnight.
*Make sure the plastic sits directly on top of the filling; this will prevent it from forming a "skin."
*Cornstarch can be substituted for flour in this recipe; however, if you do this, the recipe will no longer be gluten free.