Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg, red food coloring, vanilla extract, and vinegar, mixing until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
In a separate bowl, beat the cream cheese, powdered sugar, and vanilla extract together until smooth and creamy.
Scoop about 1 tablespoon of cookie dough and flatten it in the palm of your hand. Place about 1 teaspoon of the cream cheese filling in the center, then fold the dough around the filling to form a ball.
Repeat with the remaining dough and filling.
Place the cookie balls on the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are set but the centers are still soft.
Allow to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.