In a large bowl, beat the butter and cream cheese with a mixer on medium speed for 1 minute, until smooth. Add the granulated sugar and brown sugar and beat for 2 minutes more, until light and fluffy.
Beat in the milk, vanilla and red food coloring until the dough is evenly colored. Add a little more coloring if you want a deeper red.
In a separate bowl, whisk together the flour, cocoa powder, cornstarch, baking soda and salt. Add to the butter mixture and mix on low just until combined.Fold in 3/4 cup of the white chocolate chips with a spatula.
Cover and chill the dough for 1 hour. The cream cheese makes the dough very soft, so chilling is what gives you thick, chewy cookies instead of flat ones.
Preheat the oven to 350°F and line two baking sheets with parchment paper. Scoop the dough into 2 tbsp balls, place them 2 inches apart and press the remaining white chocolate chips onto the tops.
Bake for 10-11 minutes, until the edges are set and the tops look matte but the centers are still soft. Pull them before they brown so the red color stays bright.
Cool on the baking sheet for 10 minutes, then transfer to a wire rack. Makes about 18 cookies.