Spray a 9-inch square baking pan with nonstick cooking spray and line it with parchment.
Whisk together the flour and cocoa in a small bowl; set aside.
Combine the butter, cream cheese, granulated and brown sugars, salt and baking soda in a medium bowl. Stir with a rubber spatula until combined. Some bits of cream cheese may remain. Add the egg, vanilla extract, food coloring and vinegar; stir to combine.
Add the cocoa mixture and 1/4 cup each of the white chocolate chips and mini chips to the medium bowl; stir just until no streaks of flour remain.
Transfer the dough to the prepared baking pan and spread until smooth. Scatter the remaining 1/4 cup each of the white chocolate chips and mini chips evenly over the top.
Bake until puffed and a toothpick inserted in the center comes out with a few moist crumbs attached, 30 to 32 minutes. Let cool completely in the pan then remove and cut into 16 bars.