Preheat the oven to 350° F (180° C.) Grease and flour a 9-inch (23 cm) cast iron skillet or cake pan, or spray with baking spray that contains flour.
In a medium bowl, mix together the flour, cocoa powder, baking soda, and salt until they are well combined.
In a large mixing bowl, with an electric mixer, cream the butter, sugar, and brown sugar until they are fluffy.
Mix the eggs into the batter one at a time, then the vanilla and vinegar. Mix in the red food gel until it is fully incorporated in the batter.
Using a spoon, stir in half of the flour, being careful not to overmix. Add the white chocolate chips and the rest of the flour, stirring until it is just incorporated. Pour the batter into the prepared skillet and bake at 350° F (180° C) for about 30 minutes, or until the center is still slightly gooey, but a thermometer poked into the center reads over 160° F (71° C.)
Serve straight from the oven and top with the cream cheese frosting. To store the leftovers, remove the cookie from the cast iron pan and store at room temperature for 3-4 days.