Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
In another bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Divide the dough in half. In one half, mix in the cocoa powder until fully incorporated.
Take a tablespoon of each dough and roll them into balls. Place one vanilla ball and one chocolate ball next to each other on the prepared baking sheet.
Gently flatten them together with your hand. Repeat with the remaining dough, spacing the cookies about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
In a small bowl, mix the powdered sugar and milk to create a glaze. Drizzle the glaze over the cooled cookies.