Step 1

Lightly grease a 9 1/4-inch (23 cm) fluted tart pan with removable bottom. Whisk the flour, cornmeal, cornstarch, and salt in a medium bowl until well blended. Put the butter and confectioners' sugar in the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl using an electric handheld mixer fitted with wire beaters). Beat on medium speed until smooth and creamy, about 3 minutes. Add the rosemary and vanilla and beat on medium until blended and fragrant, about 1 minute. Add the flour mixture and beat on low speed until the dough forms moist clumps. Dump the dough into the prepared pan. Using lightly floured fingertips, press the dough into the pan to form an even layer. Make sure to press the dough into the scalloped edges to form a clean edge. Sprinkle the fleur de sel or sanding sugar, if using, evenly over the top. Using the tip of a knife or a bench scraper, score the dough all the way through, forming 16 wedges. With the tines of a fork, prick each wedge twice all the way through, starting at the widest part of the wedge and spacing them about 1/2 inch (12 mm) apart. Lightly flour the tines of the fork as necessary to prevent the dough from sticking. Slide the pan into the freezer or fridge for about 10 minutes while the oven heats. Position a rack in the center of the oven and heat the oven to 300 degrees F (150 degrees C/gas 2). Bake the shortbread until the top looks dry and very pale brown, 39 to 41 minutes. Move the pan to a rack. Using a small paring or serrated knife (I don't use a bench scraper for this because it compresses the cookies' edges), immediately recut the wedges using the scored lines as a guide. Let the shortbread cool completely before removing them from the pan. Serve the cookies with a dusting of confectioners' sugar.

Step 2

Instead of the rosemary, use one of the following combinations: Double ginger: 2 tsp. finely grated fresh ginger + 1/3 cup (1 3/8 oz./39 g) finely chopped crystallized ginger (add both with the vanilla). Cinnamon toast: 1/2 tsp. ground cinnamon added to the flour + 1 Tbs. granulated sugar mixed with 1/2 tsp ground cinnamon sprinkled over the shortbread and pressed lightly into the dough before baking. Espresso chip: 1/2 tsp. instant espresso powder (dissolved in the vanilla extract) + 1/3 cup (2 oz./57 g) finely chopped bittersweet chocolate.

Step 3

To make rectangular cookies: Line the bottom of an 8-inch (20 cm) square baking pan (the straight-sided type makes for a cleaner-looking cookie) with parchment. Prepare the dough as directed. Using lightly floured fingertips, press the dough into the pan to form an even layer. Using the tip of a knife or a bench scraper (my tool of choice), score the dough all the way through, forming 1 x 2-inch (2.5 x 5 cm) bars. With the tines of a fork, prick each bar two or three times all the way through, spacing them evenly and on the diagonal. Lightly flour the tines of the fork as necessary to prevent the dough from sticking. Proceed as directed.

Step 4

To make round cookies: Have ready two cookie sheets lined with parchment or nonstick liners. Prepare the dough as directed. Arrange a large piece of parchment on the work surface and scrape the dough onto the center. Cover with another piece of parchment and press down on the dough to flatten. Using a rolling pin, roll the dough between the parchment to a 1/4-inch (6 mm) thickness, turning, lifting, and repositioning the parchment and lightly flouring throughout the rolling. Slide the dough onto a cookie sheet and refrigerate until firm, at least 30 minutes. Remove the top piece of parchment from the chilled dough. Using a 2 1/2-inch (6 cm) round cookie cutter, cut out rounds. Using the end of a straw, punch out three holes in the center of each round. Arrange about 1 inch (2.5 cm) apart on the prepared cookie sheets. Stack the scraps, gently press together, reroll, chill, and cut as directed. Slide the cookie sheets into the fridge while the oven heats (at least 15 minutes). Bake, one sheet at a time, until the tops look dry and very pale brown, 26 to 28 minutes.