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 3-4 minutes.
Add the egg, red food coloring, vanilla extract, and vinegar to the butter mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Scoop tablespoon-sized portions of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are set. Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
While the cookies are cooling, prepare the cream cheese filling. In a medium bowl, beat together the softened cream cheese and butter until smooth. Gradually add the powdered sugar and vanilla extract, mixing until well combined and fluffy.
Once the cookies are completely cooled, spread a generous amount of cream cheese filling on the flat side of one cookie and sandwich it with another cookie. Repeat with the remaining cookies.
Serve immediately or refrigerate for up to 3 days.