1. Place flour, confectioners' sugar, granulated sugar, and salt in the bowl of a food processor. Pulse until well combined. Add butter, and pulse until coarse crumbs form. Add lime extract, and pulse just enough to mix.

2. Transfer the dough to a clean work surface, and flatten, forming a disk. Wrap the dough in plastic, and transfer to refrigerator; chill until very firm, at least 2 hours.

3. Heat the oven to 325 degrees. Line a baking sheet with a Silpat baking mat or parchment paper. Roll out the dough to a 1/8-inch thickness on a lightly floured surface. Using a 1 3/4-inch fluted cookie cutter, cut the dough into squares. Place squares on the prepared baking sheet, spaced about 1 inch apart.

4. Bake until just golden, 15 to 17 minutes. Transfer to a wire rack to cool completely.

5. To assemble the sandwiches, place 1 teaspoon key lime curd on the underside of half of the cooled squares. Top the curd with the remaining squares to form little sandwiches. Refrigerate until firm, about 20 minutes, and serve.