Place brown sugar and butter in a large, heavy bottom saucepan and set heat to medium low.
In a small bowl, mix eggs and milk together.
Add egg mixture and flour to sauce pan with sugar and butter and whisk until no lumps pf flour or sugar remain.
Turn heat to medium and cook, stirring frequently until mixture is thick, like pudding.
Remove from heat, and add vanilla.
Pour filling into blind baked deep dish pie shell. There will be extra filling, place it in a bowl and refrigerate for an afternoon snack or for those who do not like pie crust or meringue.
Using an electric mixer, beat egg whites and cream of tartar until foamy.
Gradually add 6 tablespoons of white sugar and continue beating until soft peaks form.
Turn of mixer.
Heat water, cornstarch, and 3 tablespoons granulated sugar in a small saucepan over medium heat.
Cook, stirring constantly, until mixture becomes thick and bubbly. Remove from heat.
Add hot mixture to soft peak egg whites in the mixing bowl.
Turn mixer to high and beat until meringue forms stiff peaks.
Preheat oven to 350 Degrees F.
Place meringue on top of the pie and spread out to the edges of the pie crust, this will help prevent shrinkage.
Place pie on a cookie sheet and place into preheated 350 Degree F oven. Cook for 15 to 25 minutes, or until the meringue is the color you want. I prefer light brown.
When pie is done, remove from oven and let cool for 30 minutes or so.
Place in refrigerator and allow to cool at least 8 hours, overnight would be better.
Cut and serve.