Prepare the Piecrust: Place salt and 1⁄4 cup of the water in a glass measuring cup. Stir to dissolve salt; chill 30 minutes.

Place flour in a large bowl. Cut in shortening, using a pastry blender, until crumbly. Drizzle cold salted water over flour mixture. Toss lightly with a fork until dough comes together, adding 1 to 2 tablespoons ice water, if needed.

Form dough into a disk. Wrap with plastic wrap, and chill 30 minutes.

Preheat oven to 425°F. Roll dough disk into a 14-inch circle on a lightly floured surface. Carefully transfer to a 9 1⁄2-inch deep-dish pie plate, and press into bottom and up sides of pie plate. Trim Piecrust, leaving about 1 inch around edges; reserve dough scraps. Fold edges under and crimp. Bake in preheated oven just until crust is set, about 4 minutes. Let cool 2 to 3 minutes on a wire rack, and fill in any cracks with leftover dough scraps so there are no openings in any of the crust. Cool 30 minutes. Brush lightly with beaten egg. Reduce oven temperature to 350°F.

Prepare the Filling: Melt butter in a medium saucepan over medium. Add sugar, and cook, stirring occasionally, until mixture starts bubbling, 3 to 4 minutes. Add corn syrup, and cook, stirring occasionally, until mixture starts bubbling, 3 to 4 minutes.

Remove from heat, and cool 5 minutes. Slowly whisk about 1 cup hot mixture into beaten eggs; slowly whisk beaten egg mixture back into hot sugar mixture, and whisk until thoroughly incorporated. Whisk in vanilla and salt. Stir in pecans.

Pour Filling into cooled crust. Bake at 350°F until pie is cooked through and set in the middle, 40 to 45 minutes. Cover edges with aluminum foil after 30 to 35 minutes to prevent overbrowning. (The center will rise a little at the end but will settle when cooled.) Let cool completely (about 2 hours) before slicing.