Putting the sugar through a food processor gives these cookies a wonderful lightness and fineness of texture.
Have all ingredients at room temperature, 68┬░ to 70┬░F. In a large bowl, beat on medium speed until very fluffy and well blended:
1/2 pound unsalted butter, at room temperature
1 cup sugar, processed in a food processor for 30 seconds, or superfine sugar
1/2 teaspoon salt
Add and beat until well blended:
1 teaspoon finely grated lemon zest or orange zest
1 large egg yolk
Add and beat until well combined:
1 large egg
2 teaspoons vanilla
Reduce the speed to low and beat in just until combined:
1 1/2 cups all-purpose flour
1 cup fine cornmeal
Divide the dough in half and wrap in plastic. Refrigerate until firm, at least 1 hour. (The dough can be refrigerated for up to 2 days or it can be double-wrapped and frozen for up to 1 month.) To bake, position a rack in the upper third and another in the lower third of the oven. Preheat the oven to 375┬░F. Remove 1 disk of dough from the refrigerator and cut in half. Return the unused portion to the refrigerator.
Either: Scoop the cookie dough into 1-tablespoon balls with a small ice cream scoop and roll each ball between your palms until smooth. Place the dough balls on parchment-lined cookie sheets, spacing about 2 inches apart. Using the bottom of a smooth, flour-coated glass, flatten each dough ball to about 1/8 inch thick.
Or: Lightly flour the work surface. Roll the dough to 1/8 inch thick, using an offset spatula to loosen the dough. Sprinkle the surface lightly with flour as needed to keep the dough from sticking. Cut the dough into desired shapes. Place the dough shapes on parchment-lined cookie sheets, spacing about 1/2 inch apart. Get as many dough shapes as you can out of each sheet, because the dough should be rolled only 2 times. Discard any leftover dough after the second rolling, or form the leftover dough into balls and flatten them to about 1/8 inch thick. Bake, 2 sheets at a time, until the cookies are evenly golden brown, 6 to 8 minutes; rotate the sheets halfway through baking for even browning. Using a thin-bladed spatula, immediately transfer the cookies to racks to cool to room temperature. Decorate the cooled cookies, if desired, and transfer to an airtight container.
