1. Make cookies: Arrange racks on bottom and top thirds of oven; preheat oven to 350°F. Line 2 baking sheets with parchment. In a bowl, using an electric mixer on low speed, combine sugar, flour, cocoa powder, baking soda and salt. Gradually add butter; slowly increase mixer speed to medium. Mixture will look crumbly at first, but continue mixing for about 8 minutes and it will come together in large clumps.
2. Transfer dough to a well-floured work surface and knead briefly, then press into a small rectangle. Cut dough in half. Working with one piece at a time, roll dough to 1/4-inch thickness. Using a 1/2-inch round cutter, cut circles. Gather up scraps, reroll and cut as many cookies as possible. Transfer them to baking sheets.
3. Bake cookies for 6 minutes, then rotate pans (top to bottom and front to back) and bake 6 minutes longer. Remove baking sheets from oven and place on wire racks for a few minutes to cool before transferring cookies to racks to cool completely. Repeat with remaining dough.
4. Make filling: In a large bowl, using an electric mixer on high speed, beat butter until light and fluffy, about 3 minutes. Reduce mixer speed to low and gradually add salt and confectioners' sugar. Scrape down sides of bowl. Add food coloring, drop by drop, until filling takes on desired pink hue. Transfer filling to a pastry bag. Pipe filling onto half the cookies, then sandwich them together with remaining cookies.