Step 1

Cream the butter and sugar. Cut 2 sticks cold unsalted butter into 1/2-inch cubes. Place the butter and 1/2 cup granulated sugar in a stand mixer fitted with the paddle attachment. (Alternatively, use a large bowl and electric hand mixer.) Beat on low speed to break up the butter, then increase the speed to medium and beat until fluffy and lightened in color, about 3 minutes.

Step 2

Add the egg and vanilla. Stop the mixer and scrape down the sides of the bowl with a rubber spatula. Add 1 large egg and 1 teaspoon vanilla extract, and beat on medium speed until combined.

Step 3

Beat in the flour and salt. With the mixer on low speed, slowly add 2 cups all-purpose flour and 1/4 teaspoon kosher salt, and beat until just incorporated. Use a rubber spatula to scrape down the sides of the bowl and make sure the dough is evenly mixed.

Step 4

Roll and chill the dough. Remove the dough from the bowl and shape into a smooth rectangle. Lightly dust the rectangle with flour. Place between 2 sheets of parchment paper, then roll into a rough 9x12-inch rectangle about 1/4-inch thick. Place the dough, still in the parchment, on a baking sheet. Freeze until firm, 20 to 30 minutes, or refrigerate 1 to 2 hours. Meanwhile, heat the oven and prepare the egg wash.

Step 5

Make the egg wash and heat the oven to 350ºF. Whisk the remaining 1 large egg with 1 teaspoon water together in a small bowl. Arrange 2 racks to divide the oven into thirds and heat the oven to 350°F.

Step 6

Cut the cookies. Remove the top sheet of parchment from the dough. Using a pizza cutter or knife, cut the dough into 36 (1.5x2-inch) rectangles. Arrange the cookies 1-inch apart on 2 ungreased, unlined aluminum baking sheets (not nonstick), about 18 cookies per sheet.

Step 7

Finish the cookies with egg wash and sugar. Brush the top of the cookies with the egg wash and sprinkle with 1/4 cup sanding or coarse sugar.

Step 8

Bake the cookies 10 to 14 minutes. Bake the cookies until firm and lightly golden-brown, rotating the baking sheets between racks and from front to back halfway through, 10 to 14 minutes total.

Step 9

Cool on the baking sheets for 5 minutes. Let the cookies cool for 5 minutes on the baking sheets. Transfer to a wire rack to cool completely.