In a medium saucepan over medium-low heat, stir the brown sugar and butter until butter melts and sugar dissolves.
Continue stirring and cook mixture for 2 minutes longer; remove from heat.
In a small bowl, beat egg yolks well; set aside for now.
In a large mixing bowl, combine the flour and 1 cup of the milk, mixing until smooth.
Add the egg yolks and salt and mix well again.
Add the remaining milk and thoroughly blend.
Return the sugar and butter mixture to the stove and cook on medium-low heat, slowly adding the flour mixture and stirring constantly the entire time.
Continue to stir constantly until the mixture is thickened—don’t rush this step and keep the heat low.
Remove from heat and add the vanilla.
Continue to stir the caramel syrup while it cools to barely warm and then pour into the prepared pie shell.
Top pie with meringue (see instructions below), being careful to seal the edges.
Take the back of a spoon and lift up peaks or make swirls across the top.
Bake in a preheated 350° oven for 12-15 minutes or until meringue is golden.
Allow pie to cool before serving.