Roll pie crust out about 12-inches; roll up around rolling pin and transfer to a standard pie plate.
Unroll and shape into pie plate and decorate edges as desired.
Place in the refrigerator and chill until crust is firm; at least 1 hour.
Using a medium skillet, over medium heat, melt the butter.
Allow to cook; stirring frequently until it has a nutty aroma and has browned (careful not to burn it - it should be an amber brown).
Pour into a dish and allow to cool 1 hour.
Place a baking sheet in the oven and pre-heat the oven to 350°F.
In a small mixing bowl, beat the eggs lightly to blend.
In a separate mixing bowl, whisk together granulated sugar, cornmeal, flour and salt.
Pour in browned butter, milk, vinegar and vanilla to sugar mixture and blend.
Add eggs and mix until well combined.
Pour into a prepared crust; place on a baking sheet; place in the pre-heated oven and until edges are set but center just wiggles slightly; about 45 - 55 minutes.
Remove from the oven; transfer to a wire rack to cool 30 minutes before slicing and serving.
Unused pie should be stored in the refrigerator.