Preheat oven to 350 degrees F. and line 3 baking sheets with parchment paper.
In a large bowl, use an electric mixer to combine the butter and sugars until smooth and creamy. Add the egg, vanilla and milk and beat until smooth.
Add the cocoa, flour and oats and mix just until combined. Stir in the white chocolate chips. The dough will still be slightly sticky.
Spoon rounded tablespoonfuls of cookie dough onto prepared baking sheets and press down slightly. Bake for 10 to 11 minutes, until just slightly glossy in the center (just a little!) but mostly set. Let cool for 5 minutes before removing to wire racks to cool completely.