Line a plate with parchment paper. Mix the cream cheese, powdered sugar, and vanilla until smooth, then portion into 12 small mounds and freeze for 25 minutes.
Preheat the oven to 350 F and line two baking sheets with parchment paper.
Beat the butter, brown sugar, and granulated sugar until creamy. Mix in the egg, vanilla, and red food coloring until evenly combined.
Whisk the flour, cocoa powder, cornstarch, baking soda, and salt in a separate bowl. Add the dry ingredients to the butter mixture and mix just until a soft dough forms.
Divide the dough into 12 portions. Flatten each portion, place one frozen cheesecake mound in the center, and completely enclose the filling with the dough.
Arrange the cookies at least 2 inches apart on the prepared baking sheets. Bake for 11 to 13 minutes, until the edges are set but the centers still look slightly soft.
Let the cookies cool on the baking sheets for 10 minutes before transferring them to a cooling rack. Cool for at least 20 minutes so the cheesecake centers can set.