Preheat your oven to 350°F (175°C). In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside. In a large mixing bowl, beat the softened butter and sugar until light and fluffy. Add the egg, buttermilk, red food coloring, and vanilla extract. Mix until fully incorporated.
Gradually add the dry ingredients to the wet mixture, stirring until a dough forms. The dough will be thick and slightly sticky, but it should hold together. If the dough feels too soft, chill it in the fridge for 10-15 minutes to firm up.
Using a cookie scoop or spoon, drop tablespoon-sized portions of dough onto a parchment-lined baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are set and the cookies are slightly puffed. Let them cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
While the cookies cool, prepare the frosting. In a small bowl, beat the softened cream cheese and butter together until smooth and creamy. Gradually add the powdered sugar and vanilla extract, mixing until the frosting is fluffy and spreadable. Once the cookies have cooled, spread a generous amount of cream cheese frosting on top of each one.