01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt until well combined.
03 - In a large bowl, beat softened butter and granulated sugar with an electric mixer until light and fluffy, approximately 2 minutes.
04 - Mix in egg yolk, milk, vanilla extract, and red food coloring. Beat until fully incorporated and the mixture is uniformly red.
05 - Gradually add the dry ingredient mixture to the wet ingredients. Mix on low speed until just combined, being careful not to overmix.
06 - In a small bowl, whisk together softened cream cheese, powdered sugar, and vanilla extract until completely smooth and creamy. Set aside.
07 - Roll dough into 1-inch balls, yielding approximately 24 cookies. Place on prepared baking sheets, spacing 2 inches apart to allow for spreading.
08 - Using your thumb or the back of a teaspoon, gently press a deep indentation into the center of each dough ball, being careful not to press through to the baking sheet.
09 - Spoon approximately 1/2 teaspoon of the cream cheese filling into each indentation, mounding slightly above the cookie surface.
10 - Bake for 11 to 13 minutes, or until edges are set and slightly firm but centers still appear soft.
11 - Let cookies rest on baking sheet for 5 minutes to firm up, then transfer to a wire rack to cool completely before serving.