These classy sandwich cookies will be beloved by everyone at your Easter celebration, and they'll probably be the prettiest thing on the table, too.
For the cookies, in a medium bowl, whisk the flour, cocoa powder, salt, and baking soda. In a large bowl, using an electric mixer or a stand mixer fitted with a paddle attachment, beat the sugar, butter, shortening, and vanilla on medium speed until fluffy, about 2 minutes. Scrape the sides of the bowl with a spatula. Add the corn syrup; beat until just blended. Add the dry ingredients; beat on low speed until combined.
Place the dough on a piece of plastic wrap. Form the dough into a 2 1/4-inch-wide log, rolling it on the counter to shape into a cylinder. Tighten the plastic wrap and twist the ends. Refrigerate the dough until firm, at least 2 hours.
Arrange racks in the top and bottom thirds of the oven; preheat to 350°. Line 2 baking sheets with parchment paper. Unwrap the dough. Using a sharp knife, slice the dough into 1/4-inch-thick rounds; rotate the dough as you slice to avoid flattening 1 side. Arrange the slices on the baking sheets.
Bake the cookies, rotating the sheets from top to bottom halfway through baking, until the tops appear dry, 11 to 12 minutes. Using a metal spatula, press down lightly on each cookie to flatten the top. Let cool.
For the filling, in a large bowl, using an electric mixer or a stand mixer fitted with a paddle attachment, beat the shortening, peppermint extract, and salt on medium speed until just smooth. Add the confectioners’ sugar; beat until just blended. Add 2 tbsp. room-temperature water and the food coloring. Beat the filling until just smooth and uniform in color. If you like a stiffer filling, stop now. If you prefer a fluffy filling that oozes when you take a bite, beat until fluffy, another minute or two.
To assemble the cookies, roll 3 tbsp. of the filling in your hands to form a ball; center on the bottom of 1 cookie. Press down on the filling to flatten until it almost reaches the edge of the cookie. Top with another cookie, bottom-side down. Press down gently until the filling reaches the edge. Repeat with the remaining cookies.
Place the sparkling sugar in a small bowl. Roll the edges of the cookies in the sparkling sugar.