Lemon-Buckwheat Shortbread

Stir together all-purpose flour, buckwheat flour, cornstarch, and 3/4 cup powdered sugar in a medium bowl. Combine granulated sugar, 1 cup butter, and 3/4 teaspoon salt in bowl of a stand mixer fitted with a paddle attachment; beat on medium-high speed until light and fluffy, about 2 minutes. Add egg yolk and 2 teaspoons vanilla; beat until combined, about 15 seconds, stopping to scrape down sides of bowl as needed. Gradually add flour-cornstarch mixture, beating on low speed until mixture just starts to clump together and flour is incorporated into dough, about 20 seconds.

Divide dough in half; shape each half into a 5- x 2-inch log (about 10 ounces). Wrap each log tightly in plastic wrap; chill at least 2 hours or up to 2 days.

Preheat oven to 350°F. Unwrap 1 dough log; slice crosswise into 18 (1/4-inch-thick) rounds. Arrange dough rounds 1 inch apart on a baking sheet lined with parchment paper. Bake in preheated oven until cookie edges are light golden, 10 to 12 minutes. Remove from oven; cool cookies on baking sheet 2 minutes. Transfer cookies to a wire rack to cool completely, about 30 minutes. Meanwhile, repeat process with remaining dough log.

Stir together lemon juice and 1 tablespoon water in a small bowl. Beat remaining 2 tablespoons butter with an electric mixer on medium speed until creamy, about 1 minute. Beat in remaining 1/4 teaspoon salt and remaining 1/2 teaspoon vanilla. Add remaining 3 cups powdered sugar to butter mixture, alternating with lemon juice mixture, beating on low speed until incorporated after each addition. Beat in remaining 1 tablespoon water, 1 teaspoon at a time, until consistency is thick but spreadable. Stir in lemon zest.

Transfer lemon frosting to a piping bag fitted with a 1/2-inch round tip. Turn 18 of the cooled cookies upside down; pipe bottoms of cookies evenly with frosting (about 1 tablespoon per cookie). Top with remaining 18 cookies (right side up), creating 18 cookie sandwiches total.