Roll out puff pastry on a lightly floured nonstick baking mat until it is about 1/8-inch thick. Transfer pastry to freezer; freeze until chilled, 10 to 15 minutes.
Using a 1 1/2-by-1 1/4-inch oval cutter, cut out 36 puff pastry ovals. Transfer half of the ovals to baking sheets lined with a nonstick baking mat. Using an apple corer or a 1/2-inch-round cutter, cut out the centers of the remaining half of the puff pastry ovals; discard centers or reserve for another use.
Brush tops of puff pastry ovals on baking sheet with water and top each with a puff pastry oval whose center has been removed, lightly pressing to adhere. Transfer to freezer until chilled, 10 to 15 minutes.
Preheat oven to 400 degrees. Remove baking sheets from freezer; using the tines of a fork, gently pierce inside the center of each puff pastry oval all over to prevent pastry from puffing up while baking.
Place another nonstick baking mat on top of puff pastries and transfer to oven. Bake for 10 minutes, remove baking mat from top of puff pastries and continue baking until golden brown, 5 to 6 minutes more. Remove from oven; transfer to wire rack to cool.
Place confectioners' sugar in a fine-mesh sieve and dust tops of puff pastry eggs with sugar; fill centers with lemon curd and serve.
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