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 softened butter and granulated sugar in a large bowl until light and fluffy, about 2 minutes.
04 - Mix in egg yolk, milk, vanilla extract, and red food coloring until fully incorporated.
05 - Gradually blend dry ingredients into wet mixture until just combined. Do not overmix.
06 - Whisk cream cheese, powdered sugar, and vanilla extract in a small bowl until smooth and set aside.
07 - Roll dough into 1-inch balls, placing them 2 inches apart on prepared baking sheets.
08 - Press thumb or back of teaspoon gently into center of each dough ball to form a well.
09 - Spoon approximately 1/2 teaspoon of cream cheese filling into each indentation.
10 - Bake for 11-13 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.