Step 1

Preheat the oven to 425°F with a rack in the center position.

Step 2

, To toast the flours: In a medium bowl, whisk the flours together and spread them across a large, rimmed baking sheet (a half sheet pan works well here).

Step 3

, Bake the flours, stirring once after about 5 minutes, until they've browned and smell toasty, 8 to 12 minutes. They'll smoke a little while baking; that’s OK.

Step 4

, Remove the baking sheet from the oven, turn the oven off, and let the flours cool completely.

Step 5

, To make the dough: Sift the cooled flours, salt, and baking powder through a fine-mesh sieve set over a medium bowl.

Step 6

, Place the egg yolks in the sieve and use the back of a spoon to press them through the mesh into the flour mixture. Stir to combine, then set aside.

Step 7

, In a separate large bowl, give the butter a few strokes with a flexible spatula to make sure it’s smooth and spreadable.

Step 8

, Add the granulated sugar and vanilla and beat vigorously with the spatula until the mixture is light and creamy, about 1 minute.

Step 9

, Fold in the flour mixture and stir to make a soft, well-blended dough.

Step 10

, Scrape the dough onto a sheet of plastic wrap and pat it with your dampened hands into a 7" to 8” square. Wrap tightly in the plastic and refrigerate until firm, about 1 hour (or up to 3 days).

Step 11

, Toward the end of the chilling time, preheat the oven to 350°F.

Step 12

, To prepare the cookies: Remove the dough from the refrigerator, unwrap it, and let it soften for 5 minutes or so.

Step 13

, Place the dough between two sheets of parchment and roll it about 3/8” thick and approximately 8 1/2" x 9” in size.

Step 14

, Brush the surface of the dough with a thin layer of the beaten egg. Sprinkle generously with the demerara sugar.

Step 15

, Using a knife, pastry cutter, or pizza wheel, cut the dough into 1” to 1 1/2" diamonds or rectangles.

Step 16

, Leaving the cookies in place on the parchment (don't separate them), slide both parchment and cookies onto a baking sheet.

Step 17

, To bake the cookies: Bake the cookies until they’ve puffed and the edges are browned, 18 to 22 minutes.

Step 18

, Remove the cookies from the oven; leave the oven on.

Step 19

, Cut the cookies again (retracing the lines you made earlier), but don't separate them just yet.

Step 20

, Allow the cookies to cool on the pan until you’re comfortable handling them.

Step 21

, Position one rack in the top third of the oven and one rack in the bottom third. Line a second baking sheet with parchment paper.

Step 22

, Separate the cookies and place half on the second baking sheet, spacing them evenly apart.

Step 23

, Bake both pans of cookies until they’re evenly browned all over, 10 to 12 minutes, switching racks and rotating the pans after 6 minutes. The cookies will seem soft when they come out of the oven but will crisp as they cool.

Step 24

, Let the cookies cool completely on the baking sheets.

Step 25

, Store cookies airtight at room temperature for up to five days; freeze for longer storage.