Position the racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment.
Sift the flour, cocoa, salt and baking soda together into a medium bowl. Whisk to combine and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until light and fluffy, about 3 minutes.
Add the egg and continue to mix on medium until combined, scraping the bottom and sides of the bowl as needed. Add the vanilla and food coloring and mix until combined and bright red.
Reduce the speed to low and spoon in the flour mixture. Continue to mix until just combined. Remove the bowl from the stand mixer and use a rubber spatula to ensure that all of the flour is incorporated.
Lightly flour a clean work surface. Mound the dough onto it and press into a disc. Wrap in plastic and refrigerate for 30 minutes to allow the butter to firm up.
Lightly dust your work surface with flour. Remove the dough from the refrigerator and roll to a thickness or 1/4 to 1/2 inch. Use cookie cutters to cut the dough into shapes and place on the prepared baking sheets. Brush off excess flour with a clean pastry brush if necessary. Freeze the cutouts for 15 minutes so they retain their shape when baked.
Bake until the cookies are dry and set, rotating the pans halfway through, 10 to 11 minutes. Transfer the cookies to a wire rack to cool completely.
Meanwhile, put the chocolate chips in a microwave-safe bowl. Heat in 15-second intervals, stirring well in between each, until completely melted and smooth. (Alternatively, bring 1 inch of water in a medium saucepan to a simmer over medium-low heat. Put the chocolate chips in a heatproof bowl and place over the simmering water. Allow the chocolate to melt, stirring occasionally with a rubber spatula until smooth.)
Using a fork, drizzle white chocolate over the cooled cookies to create a random zigzag pattern. Allow to set. Store the cookies in an airtight container at room temperature for up to 4 days.