Preheat the oven to 350°F. Line an 8-inch cast iron skillet with parchment paper and set aside.

Beat cream cheese, powdered sugar, egg, and vanilla extract with a beater until smooth. Set aside.

In a large bowl, combine the browned butter, brown sugar, sugar, and vanilla extract. Whisk until light and creamy.

Add the egg and whisk again until combined.

Add the flour, baking soda, and salt. Mix the dry ingredients into the wet ingredients with your hands to form a dough. If the dough is too wet, add extra flour, one tablespoon at a time, until a cookie dough is formed.

Fold in dark chocolate chips, white chocolate, and chopped Oreos.

Press half of the cookie dough evenly into the bottom of the skillet to form a base.

Spread the cream cheese mixture over the dough.

Add the rest of the cookie dough on top, being careful not to press it into the pan.

In a preheated 350°F oven, bake for 35 to 40 minutes or until golden brown on the edges and firm to the touch.

Cool for 30 minutes to an hour, then refrigerate for at least 2 hours until chilled.