01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - Whisk together flour, cocoa powder, baking soda, and salt in a medium bowl.
03 - Beat butter and sugar in a large bowl until light and fluffy, about 2 minutes.
04 - Mix in egg yolk, milk, vanilla, and red food coloring until fully combined.
05 - Gradually fold in dry ingredients until just incorporated. Do not overmix.
06 - Whisk cream cheese, powdered sugar, and vanilla extract until smooth and set aside.
07 - Roll dough into 1-inch balls, placing on baking sheets 2 inches apart.
08 - Press thumb or teaspoon back into center of each ball to form a deep well.
09 - Spoon approximately 1/2 teaspoon of cream cheese filling into each indentation.
10 - Bake for 11 to 13 minutes until edges are set but centers remain slightly soft.
11 - Let cookies rest on baking sheets for 5 minutes, then transfer to wire rack to cool fully.