Prepare the dough by whisking together flour, cocoa powder, baking powder, and salt in a bowl. In another bowl, beat butter and cream cheese until fluffy, then mix in sugar, egg, egg yolk, vinegar, vanilla, and red food coloring. Gradually combine dry ingredients, then chill dough.

Make the cheesecake filling by beating cream cheese until fluffy, then adding sugar, egg yolk, and vanilla. Mix until smooth and transfer to a piping bag.

Preheat oven to 300°F (150°C). Roll chilled dough into balls, roll them in sugar, place on baking sheets, and indent centers. Bake for 10 minutes.

After the first bake, deepen indents, pipe in cheesecake filling, and return cookies to oven for another 10 minutes until slightly puffed.

Cool cookies on baking sheets for 10 minutes, then transfer to a wire rack. Chill in refrigerator for at least 45 minutes before serving.