In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.

Beat in the egg and vanilla extract. Add the red food coloring and cocoa powder and mix until well combined.

In a separate bowl, whisk together the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.

Cover the dough and chill in the refrigerator for at least 30 minutes.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Roll the dough into 1-inch balls and place them 2 inches apart on the prepared baking sheets.

Bake for 9-11 minutes, or until the edges are set and the centers are still slightly soft.

Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

In a medium bowl, beat the softened cream cheese and butter together until smooth.

Gradually beat in the powdered sugar and vanilla extract until the frosting is light and fluffy.

Once the cookies are completely cool, frost them with the cream cheese frosting.