Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, whisk together the all-purpose flour, cocoa powder, baking soda, and salt. Set aside.
In another large mixing bowl, using an electric mixer (or whisk), cream together the softened butter and granulated sugar until light and fluffy.
Add the egg, red food coloring, and vanilla extract to the butter mixture. Mix until fully combined.
Gradually add the dry ingredient mixture to the wet ingredients, stirring until just combined. Be careful not to overmix.
Use a cookie scoop or spoon to drop rounded tablespoons of cookie dough onto the prepared baking sheet, leaving space between each cookie.
Bake in the preheated oven for about 10 minutes, or until the edges are set and the tops look slightly cracked.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack to cool completely.
While the cookies are cooling, prepare the cream cheese frosting by beating together the softened cream cheese and powdered sugar until smooth and creamy.
Once the cookies are completely cooled, frost each cookie with the cream cheese frosting using a knife or spatula.