First, whip up the pie crust: Mix the flour and salt in a bowl. Add the butter and shortening. Work the butter into the flour using a dough cutter until the mixture resembles tiny pebbles.
Add the egg with, 5 tablespoons cold water and the vinegar. Stir the mixture until just combined. Divide the dough in half and chill until needed. Once chilled, sprinkle the cutting board or counter liberally with flour. Roll half of the dough into a large circle and place in a standard pie pan. Crimp the edges according to desired look. Reserve the other half of dough for another use.
Preheat the oven to 350 degrees F.
Next, make the filling: Mix the white sugar, brown sugar, salt, corn syrup, butter, vanilla and eggs together in a bowl. Pour the pecans in the bottom of the unbaked pie shell.
Pour syrup mixture over the top. Cover top and crust lightly/gently with foil. Bake the pie for 30 minutes. Remove the foil, and then continue baking for 20 minutes, being careful not to burn the crust or pecans.
The pie should not be overly jiggly when you remove it from the oven (though it will jiggle a bit). If it shakes a lot, cover with foil and bake until set, an additional 20 minutes. Required baking time seems to vary widely with this recipe. Sometimes it takes 50 minutes, sometimes it takes 75!
Allow to cool for several hours or overnight. Serve in thin slivers.