Preheat the oven to 375° F. In the bowl of an electric mixer using the paddle attachment, cream the butter and sugars until the mixture just begins to lighten in color.
In another bowl, whisk together the flours, salt, baking soda and pecans. Set aside.
Slowly add the eggs and vanilla to the butter and sugar mixture, and mix on low speed until well blended.
On low speed, add the flour mixture, mixing until just combined.
Divide the dough in half.
Form each half into a log 13 inches long. Wrap each log in plastic wrap and chill for at least 3 hours or until firm.
Slice each log crosswise into ¼-inch thick slices and place them on a sheet pan covered with parchment paper. Using a pastry brush, brush some egg white in the middle of each cookie. Place 1 pecan half on top of each cookie, pressing gently to adhere.
Bake the cookies for about 9 to 12 minutes or until the bottoms and edges are light brown. Allow the cookies to cool on the sheet pan for 5 minutes before removing and placing them on cooling racks.