Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a bowl, whisk together flour, cocoa powder, baking soda, and salt; set aside.
In a large mixing bowl, 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, mixing until combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Scoop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes or until the edges are set but the centers are soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
In a separate bowl, beat the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy to make the frosting.
Once the cookies are completely cooled, spread a generous layer of frosting on each cookie.