Heat oven to 375°F; line sheets with parchment.
Cream butter and sugar about 3 minutes until fluffy; add eggs individually, then coloring and vanilla.
Separately whisk flour, cocoa, baking soda, and salt.
Gradually mix dry into wet just until combined.
Beat cream cheese and powdered sugar smooth in small bowl; transfer to piping bag or zip-top bag with snipped corner.
Drop rounded tablespoons dough 2 inches apart on sheets.
Pipe little cream cheese mixture on each; toothpick-swirl into red dough to marble.
Bake 9-11 minutes until edges set and centers slightly underdone.
Cool on sheet 5 minutes; transfer to rack to cool completely.