Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together butter, granulated sugar, and brown sugar until light and fluffy.
Add eggs, vanilla, and red food coloring. Mix until combined.
In another bowl, whisk together flour, cocoa powder, baking soda, and salt. Gradually mix into wet ingredients.
In a separate bowl, mix cream cheese and powdered sugar until smooth. Chill for 10 minutes.
Scoop a tablespoon of cookie dough, flatten slightly, add a small dollop of cream cheese mixture, and seal with more dough to cover.
Place cookies on baking sheet and bake for 10–12 minutes, or until edges are set.
Cool on the pan for 5 minutes before transferring to a wire rack.