Prepare the Cream Cheese Filling:

1. Mix the Filling: In a small bowl, beat together the softened cream cheese, powdered sugar, and vanilla extract until smooth.
2. Chill: Scoop teaspoon-sized portions onto a parchment-lined tray and freeze for at least 1 hour, or until firm.

Prepare the Cookie Dough:

3. Mix the Dry Ingredients: In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt.
4. Cream the Butter and Sugars: In a large bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy.
5. Add the Wet Ingredients: Mix in the egg, vanilla extract, white vinegar, and red food coloring until well combined.
6. Combine the Mixtures: Gradually add the dry ingredients to the wet mixture, alternating with the milk, until a smooth dough forms.
7. Chill the Dough: Cover and refrigerate for at least 1 hour.

Assemble the Cookies:

8. Preheat Oven: Set to 350°F (175°C). Line a baking sheet with parchment paper.
9. Stuff the Cookies: Take a tablespoon of dough, flatten it in your palm, place a frozen cream cheese ball in the center, and wrap the dough around it. Roll into a smooth ball.
10. Bake: Arrange cookies 2 inches apart on the baking sheet and bake for 12-14 minutes, until edges are set.

Cool and Serve:

11. Cool on Baking Sheet: Let cookies sit for 5 minutes before transferring to a wire rack.
12. Serve: Enjoy warm for a gooey center or chilled for a firmer texture.