Place a rack in the center of the oven and preheat to 400°. In a medium bowl, combine the flour, oil, milk and 1/4 teaspoon salt, stirring with a fork until the dough just comes together. Pat the dough flat and place between 2 sheets of parchment or wax paper. Roll out the dough to an 11-inch round. Transfer the dough to a 9-inch pie plate, fitting it into the pan without stretching; crimp the edges of the pie shell. Using a fork, gently prick the bottom of the crust a few times and refrigerate.
In a large bowl, whisk together the butter, sugar, corn syrup, eggs, 2 tablespoons plus 1 teaspoon vanilla and the remaining 1/4 teaspoon salt.
Cover the bottom of the piecrust evenly with the pecans and pour in the filling. Bake the pie, rotating it halfway through, until the crust is golden and the filling is set in the middle, about 45 minutes. Let the pie cool on a wire rack for at least 45 minutes.
Meanwhile, using an electric mixer, beat the heavy cream on high speed until soft peaks form, 2 to 3 minutes. add the remaining 1/4 teaspoon vanilla and beat until incorporated, about 10 seconds more. Serve with the pie.