Preheat the oven to 350˚F (180˚C). Line large baking sheets with parchment paper or silicone baking mats and set aside.
In a large mixing bowl, whisk together the flour, baking soda, and salt until well combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl using a handheld mixer, beat the butter and cream cheese together until well combined.
Mix in the granulated sugar and brown sugar for 1 to 2 minutes, or until well combined.
Mix in the egg and vanilla extract, making sure to stop and scrape down the sides of the bowl as needed.
Mix in the dry ingredients until just combined, then gently fold in the white chocolate chips and chopped Oreos.
Using a 1 1/2-tablespoon cookie scoop, scoop the cookie dough onto the prepared baking sheets, making sure to leave 1 1/2 to 2 inches (4 to 5 centimeters) between each one. Gently press each ball of cookie dough down to slightly flatten it (if desired, top with a few more pieces of chopped Oreos).
Bake for 9 to 12 minutes, or until the tops of the cookies are set. Remove from the oven, and allow the cookies to cool on the baking sheets for 5 to 10 minutes, then carefully transfer the cookies to a wire rack to cool completely.
Store the cookies in an airtight container at room temperature for up to 1 week.