01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - Whisk flour, cocoa powder, baking soda, and salt in a medium bowl until evenly blended.
03 - Beat softened butter and granulated sugar in a large bowl until light and fluffy, approximately 2 minutes.
04 - Mix in egg yolk, milk, vanilla extract, and red food coloring until fully incorporated.
05 - Gradually fold in the dry ingredients until just combined, being careful not to overmix.
06 - Whisk cream cheese, powdered sugar, and vanilla extract in a small bowl until smooth and creamy. Set aside.
07 - Roll dough into 1-inch balls, approximately 24 total. Arrange on prepared baking sheets with 2 inches of space between each ball.
08 - Press a gentle indentation into the center of each dough ball using your thumb or the back of a teaspoon.
09 - Spoon approximately 1/2 teaspoon of the 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 a wire rack to cool completely before serving.