Preheat the oven to 350°F.
Brown butter in a small saucepan over medium heat. Cook and swirl butter until the butter begins to turn a toasted golden brown color. Remove from heat immediately and transfer to a dish to cool.
Whisk together the sugar, cornmeal, flour, and salt in a medium bowl.
In another mixing bowl, combine the eggs, milk, vanilla extract, and vinegar. Stir the cooled butter mixture into the milk/egg mixture.
Pour wet ingredients into the mixing bowl with the dry ingredients and stir or whisk to combine well.
Pour the pie filling into a 9-inch unbaked pie crust.
Bake for 45 to 50 minutes, checking the pie after 20 minutes and covering (between 20 to 30 minutes, when pie and crust are browned) with aluminum foil to prevent the crust and top of the pie from over-browning.
Remove the pie from the oven when the center is just slightly jiggly.
Allow the pie to cool completely before slicing.
Dust lightly with powdered sugar and serve.