Sift the flour, cocoa powder, baking soda and 1/8 teaspoon salt into a medium bowl.
Beat the butter and granulated sugar in the bowl of a stand mixer fitted with a paddle attachment (or a large bowl if using a hand mixer) on medium speed just until combined. Beat in the egg yolk just until combined. Beat in the food coloring and vanilla until the color is evenly distributed, scraping down the bowl as needed. Reduce the mixer speed to low and gradually add the flour mixture. Beat just until the dough comes together. Form the dough into two 1-inch-thick disks, wrap tightly in plastic and refrigerate until firm, about 2 hours.
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Lightly dust a sheet of parchment paper with flour. Unwrap one disk, place it on the paper and cover with a large sheet of plastic wrap. Roll the dough out to 1/8 inch thick. Peel off the plastic wrap and, using a 2 1/2-inch round or square cookie or biscuit cutter, cut out the dough. Place the cut-outs on the prepared baking sheets, spacing them 1 inch apart (about 12 cookies per sheet). Gather the scraps, chill until firm, roll again and cut. Repeat with the remaining disk.
Bake the cookies until brick-red and set, 8 to 10 minutes, rotating the baking sheets halfway through. Let the cookies cool on the sheets for 3 minutes, then transfer to a wire rack to cool completely.
Line a rimmed baking sheet with parchment. Scoop a generous 1/4 cup ice cream into a 2 1/2-inch round or square cookie or biscuit cutter set on the parchment. Smooth the top flat and remove the cutter. Repeat with the remaining ice cream to form 12 to 14 disks or squares, spaced evenly apart. Freeze until firm, about 2 hours.
Place 1 portion of ice cream on 1 cookie and top with another cookie. Trim off any ragged edges of ice cream. Repeat with the remaining cookies and ice cream. Freeze for at least 4 hours or overnight.
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