Preheat the oven to 325 degrees F. Cut a piece of foil 8 by 16-inches. Butter the corners and sides of an 8-by-8-inch baking pan. Line the pan with the foil, leaving an overhang on two sides.
Beat the butter and sugar in the bowl of an electric mixer fitted with the paddle attachment on medium-high speed until light and fluffy, about 5 minutes. Reduce the speed to medium and add the egg yolk, syrup, vanilla extract and vanilla bean seeds if using. Reduce the speed to low, add the flours and salt, all at once, and beat until just combined. Add the walnuts and continue to mix until fully combined.
Using your hands, drop the dough in pieces evenly into the prepared pan. Flour your hands lightly and press the dough together and into the corners of the pan. Put a piece of waxed paper on top of the dough and use something square and heavy-another pan, a pound of cold butter-to press the dough into the pan and make a smooth, even top. Chill until firm, about 30 minutes.
When it is firm, use a fork to score the dough all over. Bake until deep golden brown and starting to pull away from the sides of the pan, about 45 minutes. Cool completely on a rack, about 2 hours, then wrap with plastic wrap, and let sit at room temperature overnight.
Place a lightweight cutting board or a baking rack over the top of the pan. Flip and set on the counter. Gently pull the pan from the foil and the foil from the pan to lift off the pan. Gently peel the foil off the bar. Place another lightweight cutting board on top, and flip the bar right-side-up.
Using a sharp, serrated knife, slice the square in half. Then slice each half into 8 bars.