Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the flour, cocoa powder, baking powder, and salt.
In another bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the egg, milk, vanilla extract, and red food coloring until well combined.
Gradually add the dry mixture to the wet, mixing until combined but not overmixed.
Using a cookie scoop or tablespoon, drop dough onto a lined baking sheet, spacing them about 2 inches apart.
Using your thumb or the back of a spoon, make an indentation in the center of each cookie.
Bake the cookies for 10-12 minutes or until the edges are set.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.
Meanwhile, in a small bowl, combine softened cream cheese and powdered sugar until smooth.
Once cooled, fill each cookie indentation with the cream cheese mixture.
Serve and enjoy your delicious red velvet thumbprint cookies!