Add flour, sugar, cocoa powder, and salt to the bowl of a food processor. Pulse until mixed.
Add butter and food coloring. Run the food processor until the mixture forms a dough ball. You may need to add a drop or two of water. Wrap the ball in plastic wrap and chill it in the fridge for 1 hour.
When ready to bake, preheat the oven to 325°F and line a large baking sheet with baking paper.
Turn the dough out onto a lightly floured surface.
Roll out dough to about 1/4-inch thickness and cut out 24 rounds with a small round cookie cutter.
Transfer the cookies to the lined baking sheet and bake for 12-15 minutes, or until the centers are set. Allow to cool on the baking sheet for 10 minutes, then transfer to a rack and cool completely (approximately 30 minutes).
To Make The Drizzle:
Melt the white chocolate melts according to package directions.
Add oil and mix until combined.
Transfer the mixture to a squeeze bottle and drizzle over the cooled cookies. Let stand until set, approximately 20 minutes.