In a medium bowl, stir together flour, sugar, cocoa powder, and salt. Using a pastry blender, cut in butter and food coloring until mixture resembles fine crumbs and starts to cling together (it will take a while for the dough to come together). Form mixture into a ball, kneading until smooth.
Place cookies in a single layer in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.