Preheat the oven to 325°F. In a food processor, combine the flour, sugar, cocoa powder, and salt. Cover and process with on/off turns until combined. Add the butter, red food coloring and emulsion. Process with on/off turns until the mixture resembles fine crumbs. Then continue to process until the mixture begins to clump together.
Scoop the dough onto a lightly floured surface and knead lightly until nearly smooth. Roll or pat dough to a ½ inch thickness. Using a floured 1½ inch round cutter, cut out the dough. Place the cutouts 1-inch apart on an ungreased cookie sheet. Press the scraps together, re-roll and cut more cookies.
Bake in the preheated oven for 20 to 25 minutes or until the centers are set. Transfer the cookies to a wire rack and let cool.
In a small, heavy saucepan, melt the white chocolate and shortening over low heat, stirring constantly. Dip half of each cookie into melted chocolate. If desired, sprinkle with festive sprinkles, nonpareils or chopped pistachios. Let stand on waxed paper until set.
Notes
I make the dough using a food processor, which is easiest because it takes a bit of processing to allow the crumbs to clump together and become the proper consistency for rolling. If you'd like to try the hand-mixing method: In a medium bowl, stir together flour, sugar, cocoa powder, and salt. Using a pastry blender, cut in butter, food coloring and emulsion 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.
I use gel paste food coloring to color my cookies (instead of the liquid food coloring). It's more concentrated, and you can add more of it to get a deeper color without adding liquid to the mixture. Don't overdo it though, or you'll end up with red stained fingers as you eat your cookies!
For storing: Place the 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.
These cookies are a shortbread-type cookie and not a really sweet cookie. They have a hint of the red velvet flavor that you might be hoping for. I'd say they are more of a pretty cookie... and the white chocolate drizzle helps make them sweeter and more festive.