Roll pie crust out about 12-inches then roll up around rolling pin and transfer to a standard pie plate. Unroll and shape into pie plate and decorate edges as desired. Chill until crust is firm, at least 1 hour.
Melt butter in a medium, light-colored skillet. Let 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 let cool 1 hour.
Place a baking sheet in oven and preheat oven to 350 degrees.
In a mixing bowl beat 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 prepared crust and bake on baking sheet in preheated oven until edges are set but center just wiggles slightly, about 45 - 55 minutes.
Transfer to a wire rack to cool 30 minutes before slicing and serving. Store pie in refrigerator.
*My favorite pie crust recipe is the one I've used here, omitting the sugar (since this pie is already plenty sweet). Prepare through step 2 as directed then follow recipe here as directed.