Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.
Beat in the vanilla extract and the egg until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the semi-sweet and white chocolate chips until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are set but the centers are still soft.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.