Preheat oven to 400 degrees. Mix flour, sugar and salt in a mixer with the paddle on slow speed. Scatter the butter over the mixture and mix until it resembles coarse cornmeal. Add egg white mixture and mix on low speed until dough sticks together. Remove from bowl and shape into a 4-inch diameter disc. Dust lightly with flour and wrap with plastic. Refrigerate for 1 hour.

Dust counter with flour and place dough disc on top, flip over and dust with more flour. Roll to a 13-inch circle and transfer to a 9-inch pie pan. Press the dough snugly into the corners of the pan and flute the edge. Place shell in refrigerator again for 1 hour. Remove and use fork to poke holes in the surface. Place pie weights or uncooked beans inside shell all the way to the top. Return to the refrigerator for 1/2 hour, then move to the preheated oven and bake for 15 minutes. Remove pie weights and bake for an additional 5 minutes. Remove from oven, brush with egg yolk mixture and bake for 1 more minute.

Melt butter in a heatproof, non-reactive bowl set inside a bain-marie or double boiler with water heated to simmer. Remove bowl from bain-marie and mix in sugar and salt until well incorporated. Beat in the eggs, corn syrup and vanilla. Place bowl back in bain-marie and stir until it reaches a temperature of 130 degrees. Stir in pecans. Pour mixture into warm pie shell and place in oven. Bake for 50 to 60 minutes. The center of the pie will set and have a gelatin-like feel. Transfer to a pie rack and let cool for 2 hours.

Slice pie into 8 slices and serve immediately.