PIE DOUGH (make half of recipe): Whisk flour, sugar,and salt in a bowl. Using a dough blender,two forks,or your fingers,cut butter into flour mixture,forming pea-size crumbles. Add water.
Work dough until smooth but with visible flecks of butter. (Alternatively, pulse ingredients in a food processor.) Divide dough in half and flatten into disks. Wrap disks in plastic wrap. Chill 1 hour before using.
Heat oven to 375°. On a lightly floured surface, roll dough into a 12″ round. Fit into a 9″ pie plate. Trim edges and crimp. Chill 30 minutes. Using a fork,prick the dough all over. Line dough with parchment paper and fill with pie weights or dried beans. Bake 15 minutes. Remove paper and weights. Let cool.
MAKE the FILLING: Melt butter in a 10″ skillet over medium heat. Cook until butter is dark golden brown with dark brown flecks and it
gives off a nutty aroma. 20–22 minutes. Remove from heat. Let cool. Whisk sugar and eggs in a bowl until pale and fluffy.
Stir in browned butter, plus corn syrup, vanilla, and salt until smooth. Fold in walnuts and pour filling over dough; using a rubber spatula, spread into an even layer. Bake until just set in the center, about 40 minutes. Transfer pie to a rack and let cool completely before serving.
MAKE the TOPPING: Whip heavy cream and sugar in a bowl until stiff peaks form. Fold in sour cream and vanilla. Serve slices of pie with a dollop of sour whipped cream.