These sweet and savory shortbread cookies get a pleasant brininess from roasted, seasoned seaweed, a common ingredient in Asian sweets. Slideshow: More Make-Ahead Desserts
Preheat the oven to 300°. Grease a 9-inch-square baking pan and line with parchment paper, leaving a few inches of overhang at 2 ends. Line a rimmed baking sheet with parchment paper.
In a medium bowl, whisk the 2 flours with the kosher salt. Place the seaweed in a small resealable plastic bag and lightly crush with a rolling pin. Whisk 1/2 cup of the crushed seaweed into the dry ingredients.
In a large bowl, using a hand mixer, beat the butter at moderately high speed until light and fluffy, about 2 minutes. Add the 1/2 cup of sugar and beat until the mixture is smooth and pale yellow, scraping down the side of the bowl as needed, about 2 minutes more. Beat in the dry ingredients; the mixture will resemble wet sand and hold together when pressed. Transfer the dough to the prepared pan and pat into an even layer. Bake for about 1 hour and 20 minutes, or until the shortbread is a light golden brown. Let cool on a rack for 5 minutes.
Using the parchment overhang, transfer the shortbread to a work surface. Brush the top with the egg wash and sprinkle with sugar, flaky sea salt and the remaining 3 tablespoons of crushed seaweed. Cut the shortbread square into thirds, then slice crosswise into 3/4-inch-wide cookies. Transfer to the prepared baking sheet and bake until golden brown on top, about 10 minutes. Transfer the cookies to a rack and let cool completely before serving.
The cookies can be stored in an airtight container for up to 1 week.
Kimjaban, a crumbled seaweed snack seasoned with sesame oil, salt and sugar, is available at Asian grocery stores and on amazon.com. You can also use sheets of seasoned roasted seaweed.