Sift the flour, cocoa powder, baking soda and salt into a medium bowl. Beat the sugar and butter with an electric mixer on medium speed in a large bowl until just combined. Beat in the egg yolk until just combined. Beat in the food coloring and vanilla until well blended, scraping down the sides of the bowl occasionally. Reduce the mixer speed to low and beat in the flour mixture until the dough just comes together. Form the dough into 2 disks, wrap tightly in plastic wrap and refrigerate until firm, about 2 hours.
Position oven racks in the top and bottom thirds of the oven and preheat the oven to 350 degrees F. Line 2 baking sheets with parchment.
Sandwich 1 disk of dough between 2 sheets of parchment dusted with flour and roll the dough 1/8 inch thick. Cut out rounds using a 2 1/2-inch cookie or biscuit cutter and put on the prepared baking sheets about 1 inch apart (about 12 cookies per sheet). Repeat with the second disk of dough.
Bake the cookies, rotating the baking sheets halfway through, until set and brick red, 8 to 10 minutes. Let the cookies cool on the sheets for 3 minutes, then transfer to a wire rack to cool completely. The cookies can be stored at room temperature in an airtight container for up to 3 days.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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