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TO MAKE THE LEMON-CURD FILLING: In a medium stainless-steel or other non-reactive heatproof bowl, whisk together the lemon juice, lemon zest, lime juice, lime zest, egg, egg yolk, and sugar.
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Bring a pot of water to a gentle simmer.
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Place the bowl over the pot, making sure that the bowl isnt touching the water.
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Rotate the bowl from time to time, and stir the mixture occasionally.
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Cook it for about 25 minutes, until its very thick.
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Using a fine-mesh sieve, strain the lemon curd, and cool to room temperature.
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Transfer the mixture to a blender or a food processor fitted with a metal blade.
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Add the butter 2 tablespoons at a time, mixing a few seconds after each addition, just long enough to incorporate the butter.
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Chill the curd for 30 minutes to an hour, or up to 2 days.
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TO MAKE THE COOKIE DOUGH: In a small skillet, over medium-high heat, toast the fennel seeds until they release their aroma.
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In a spice grinder or a mortar and pestle, grind the seeds coarsely.
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In a food processor fitted with a metal blade, process the almonds and half of the powdered sugar until theyre a fine meal.
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Add the cornmeal and fennel seeds, and pulse to combine.
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In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and lemon zest on low speed for about 2 minutes.
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Turn the mixer off, and add the almond mixture and remaining powdered sugar.
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Turn the mixer up to medium, and mix another 34 minutes, until the mixture is light and fluffy, scraping down the sides of the bowl as needed.
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Add the egg yolks one at a time, mixing the first in well before adding the second.
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Turn the mixer off, and add the flour in 3 batches, mixing on low speed until its just combined.
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Gather two-thirds of the dough into a ball, and flatten it into a disc to use for the bottom cookies.
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Gather the remaining dough into a ball, and flatten into a disc to use for the top cookies.
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Wrap the discs with plastic, and chill them for about 30 minutes to an hour, until firm.
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Adjust the oven racks to the lower and middle positions, and preheat the oven to 350 degrees.
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TO ROLL OUT THE BOTTOMS: Remove the larger piece of dough from the refrigerator.
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On a lightly floured surface, roll the dough out until its 1/8 inch thick.
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Using a 2 1/2-inch round cookie cutter, cut out the cookies as closely together as possible, and place them 1/2 inch apart on 12 parchmentlined baking sheets.
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Gather the scraps, roll out the dough, and cut out more cookies in the same manner.
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Chill them for about 10 minutes, until firm.
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TO ROLL OUT THE TOPS: On a lightly floured surface, roll out the remaining dough until its 1/4 inch thick.
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Using a 1 1/2-inch round cookie cutter, cut out the cookies, cutting as closely together as possible, and place them 1/2 inch apart on a parchment-lined baking sheet.
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30
Gather the scraps, roll out the dough, and cut out more cookies in the same manner.
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31
Using a 3/4-inch round cookie cutter, cut out the centers of the cookie tops.
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(Reserve and bake the cut-out centers into tiny button cookies, or gather them together, chill, and reroll to use for additional cookies.)
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Chill tops for about 10 minutes, until firm.
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TO BAKE THE BOTTOMS: Bake for about 15 minutes, rotating the baking sheet halfway through.
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TO BAKE THE TOPS: Poke the ends of the fennel fronds (you may need more than one frond) into each cookie top, and bake for about 1820 minutes, rotating the baking sheet halfway through.
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Allow the cookies to cool for at least 30 minutes.
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Flip the bottoms over.
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Using a spoon or a pastry bag fitted with a #2 tip, spoon or pipe about 1 teaspoon of the lemon filling onto the center of each bottom cookie.
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Sift a fine layer of powdered sugar over the tops.
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40
Center the top cookie over the filling, and press it down gently.
