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 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 blend dry ingredients into wet mixture until just combined. Avoid overmixing.
06 - Whisk cream cheese, powdered sugar, and vanilla extract in small bowl until smooth and creamy. Set aside.
07 - Roll dough into 1-inch balls, approximately 24 total. Arrange on prepared baking sheets 2 inches apart.
08 - Press center of each dough ball with thumb or teaspoon back to form deep well.
09 - Spoon approximately 1/2 teaspoon cream cheese filling into each indentation.
10 - Bake for 11-13 minutes until edges appear set and slightly firm.
11 - Let cookies rest on baking sheet 5 minutes. Transfer to wire rack and cool entirely before serving.