Par-bake the crust. Fit the pastry into a 9-inch pie pan, prick the bottom with a fork, then line with foil or parchment and fill with pie weights. Bake at 400°F for 12 to 15 minutes. Remove the weights and bake for 2 to 3 minutes more to set the bottom. Set it aside to cool and reduce the oven temperature to 325 F.
Prepare the filling. While the pie shell cools, combine the sugars, flour, and cornmeal in a medium saucepan and whisk to blend. Add the milk and butter and place the pan over medium-low heat. Cook until the sugars have dissolved, the butter has melted, and the mixture is smooth. Set aside to cool slightly.Beat the eggs with the salt and vanilla, then whisk them into the sugar mixture, blending thoroughly. Whisk in the vinegar.
Fill the pie pastry. Pour the mixture into the cooled pie shell and carefully place the pie on a baking sheet.
Bake. Transfer the pie to the oven and bake at 325°F for 45 to 55 minutes, or until the top is golden brown and puffy, with only a slight jiggle in the center. As for timing, if you open the oven to carefully add a pie shield, it will impact the total time. You can also start with a pie shield, then remove it for the last 15 to 20 minutes.
Cool the pie on a rack before slicing, and store leftovers, covered, in the fridge.