Step 1

Preheat oven to 425°F.

Step 2

Roll pie crust into a 13-inch circle, about 1/8 inch thick, on a lightly floured surface. Transfer to a 9-inch pie pan. Fold the overhanging pastry under itself along the rim of the pan. Press a fork around the edge or flute it by pinching with your finger and thumb to crimp the folded dough.

Step 3

Separate 1 egg, placing the white in a small bowl. Place the yolk in a medium bowl. Whisk the egg white with a fork until frothy. Brush the crust with the egg white. Add any remaining white to the bowl with the yolk. Bake the crust until pale golden, about 10 minutes.

Step 4

Meanwhile, add the remaining 2 eggs to the bowl with the yolk and white and whisk until smooth. Add flour and whisk until smooth. Add butter, buttermilk, brown sugar, cane (or corn) syrup and vanilla and whisk until well incorporated. Stir in pecans.

Step 5

Reduce oven temperature to 350°. Add the pecan mixture to the crust. Bake the pie until the filling is set and golden brown, about 45 minutes. Transfer the pie to a rack and let cool to room temperature, about 1 hour.