Place the softened butter in a mixing bowl.
Beat the butter until smooth and creamy.
Add the brown sugar and mix until well combined.
In a small bowl, combine the milk and vanilla extract.
Add the milk mixture to the butter mixture and whisk until smooth.
Add the flour, cocoa powder, baking powder, and salt.
Mix until a soft dough forms.
In a separate bowl, combine the cream cheese and powdered sugar until smooth.
Add the cocoa mixture to the cookie dough.
Add the red velvet mixture and white chocolate chunks, then fold until evenly distributed throughout the dough.
Scoop portions of dough onto a lined baking sheet and top with small dollops of the cream cheese mixture.
Bake at 350°F (175°C) for 10–12 minutes, or until the cookies are set around the edges.
Allow the cookies to cool slightly before serving.