Whisk together the flour, sugar, and salt in a large bowl. Add the butter and mix with a pastry blender or fork until the mixture resembles coarse meal and the butter is the size of small peas.

Add 1 tablespoon of water and continue mixing. Add more water as needed, 1 tablespoon at a time, until a dough forms.

Wrap the dough tightly in plastic wrap. Refrigerate for at least 2 hours.

Remove the dough from the refrigerator. If necessary, let it sit at room temperature for 10 to 15 minutes until slightly softened but still cold.

Lightly flour a work surface. Roll out the dough into a circle about 1/8-inch thick.

Transfer the dough to a 9-inch pie plate. Trim and crimp the edges as desired. Place the pie plate in the refrigerator while you make the filling.

In a large bowl, combine the cooled butter, eggs, sugar, brown sugar, milk, cornmeal, vanilla, and salt. Mix in the peanut butter until thoroughly combined and smooth.

Transfer the filling to the chilled pie plate, spreading evenly.

Bake 55 to 60 minutes, or until the pie is golden brown and the filling is set. Cool completely before serving.