A double dose of lemon makes these frosty ice cream sandwiches irresistible. The cookies have lemon zest, lemon juice and lemon extract, and before they're sandwiched with vanilla ice cream, they're smeared with tangy lemon curd.
Spoon the ice cream into a rimmed baking sheet and spread to 1/2-inch thickness. Freeze until firm, 2 to 3 hours. Use a 3-inch round cookie cutter to cut the ice cream into 12 rounds, reshaping the ice cream "sheet" as needed. Keep frozen.
Preheat the oven to 350 degrees F. Line 2 rimmed baking sheets with parchment paper.
Stir together the flour, baking soda, baking powder, cornstarch and salt in a large bowl; set aside.
Beat the butter and granulated sugar with an electric mixer at high speed until creamy. Add the egg, and beat until the yellow disappears. Beat in the lemon zest, juice and extract.
Add the flour mixture in 2 batches and beat until combined. Roll the dough into twenty-four 2-inch balls. Roll the balls in coarse sugar, if using, and place on the prepared pans. Use the bottom of a glass to press down the dough balls.
Bake until the cookies are set and lightly golden on the bottoms, 15 to 18 minutes. Remove to wire racks to cool completely.
To assemble the sandwiches, spread 1 to 2 tablespoons lemon curd on the flat sides of 12 cookies. Sandwich an ice cream round between 2 cookies (one lemon curd-coated and one uncoated). Roll the edges in the sprinkles. Wrap and freeze the ice cream sandwiches until ready to serve.