Preheat your oven to 350°F (177°C). Line a baking sheet with parchment paper or a silicone mat to prevent sticking and ensure easy cleanup.
In a bowl, whisk together the all-purpose flour, baking soda, salt, and unsweetened cocoa powder; set this mixture aside.
In another bowl, cream the softened unsalted butter and granulated sugar until light and fluffy.
Add the large egg to the butter-sugar mixture, then blend well.
Mix in the vanilla extract and red food coloring until the dough is a uniform red shade.
Reduce the mixer speed to low and gradually add the flour mixture to the wet ingredients.
Bring the cookie dough together with your hands and roll it into smooth balls, about 1 inch in diameter.
Place the dough balls on the lined baking sheet, giving them space and gently flattening them a bit before baking.
Bake in the preheated oven for 10-11 minutes, or until the edges are set.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
In a large bowl or stand mixer, beat the softened cream cheese and unsalted butter together until smooth.
Decrease the mixer speed to low and add powdered sugar, vanilla extract, and a pinch of salt. Blend until combined.
Increase the mixer speed to medium-high and beat for 2 minutes.
Spread the cream cheese frosting generously onto each cooled cookie.