Beat together cream cheese, sugar, sour cream, and vanilla extract. Using a tablespoon, scoop out 12 individual dollops onto a parchment-lined baking sheet. Freeze for 1-2 hours.
In a large bowl, mix together butter, sugar, vanilla extract, and milk until well combined. Sift in flours, cocoa powder, baking powder, and baking soda. Mix until well combined but not over-mixed. Place in fridge for 30-60 minutes.
Once cooled, scoop heaping tablespoons of cookie batter into hands covered in powdered sugar. Add 1 dollop of the frozen cheesecake mixture and add another tablespoon of batter on top. Roll into a ball so the cheesecake mixture is completely encased. Roll in powdered sugar and place on a parchment-lined baking sheet. Repeat until all the batter is gone. Separate each cookie by 1 ½ – 2 inches.
Bake cookies in a preheated 350°F oven for 1-12 minutes or until slightly golden on the sides. Allow cooling on baking sheet for 15 minutes before moving to a cooling rack.