Preheat oven to 375 F. Line two baking sheets with parchment paper.
In a small bowl, whisk together the flour, baking soda, salt, and cocoa powder; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat together butter and sugars until fluffy, about 3 minutes. Add the egg and vanilla and beat until combined. Beat in red food coloring. Reduce speed to low and add flour mixture, beat to combine. Fold in 1/2 cup white chocolate chips.
Roll a heaping tablespoon of dough into a 1½-inch ball, roll the ball and place on the prepared baking sheet. Repeat with the remaining dough, spacing the balls about 2 inches apart.
Bake, rotating sheets halfway through, until cookies are set in center and begin to crack, 10 to 12 minutes. Let cookies cool on sheets for 3 minutes before transferring cookies to wire racks to cool completely.
In a microwave safe bowl melt remaining 1/4 cup of white chocolate chips. Drizzle the white chocolate over the cooled cookies. Let the cookies set until the chocolate hardens. Store in airtight container.