For this shortbread, chef William Werner makes his own peanut butter. He recommends buying pure peanut butter without added sugar, preferably from a shop where it's made on-site. Slideshow: Sandwich Cookies
Sift both flours with the cocoa and salt into a bowl. In a stand mixer fitted with the paddle, beat the butter with the 1/2 cup of sugar and vanilla seeds at medium speed until smooth but not fluffy, 1 minute. Beat in the dry ingredients in two additions at low speed. Scrape the dough onto a work surface and shape it into a disk. Wrap in plastic and refrigerate until firm, at least 1 hour.
Roll out the dough between 2 large sheets of parchment paper to a 9-by-16-inch rectangle, about 1/4 inch thick. Slide the dough onto a large baking sheet and refrigerate until firm, about 15 minutes.
Preheat the oven to 350°. Line 2 large baking sheets with parchment paper. Remove the top sheet of paper from the dough. Cut the dough into 4-by-1 1/2-inch rectangles. Sprinkle both sides with sugar and transfer them to the prepared baking sheets. Bake for 14 minutes, until barely firm. Let the cookies cool on the baking sheets for 10 minutes, then transfer them to a rack to cool completely.
In a bowl, using an electric mixer, beat the peanut butter and confectioners' sugar until smooth. Beat in the butter, cream, vanilla and salt. Wrap with plastic; refrigerate until firmed up, 15 minutes.
Turn half of the cookies bottom side up and spread each one with 1 tablespoon of the filling. Top with the remaining cookies and press lightly. Refrigerate until firm before serving, storing or gifting.
The cookies can be refrigerated in an airtight container for up to 5 days.