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With a standing mixer or a hand mixer, cream the butter and cream cheese together until light and fluffy.
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Add in the granulated sugar and brown sugar, and continue to cream the mixture until light and fluffy.
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Add in the egg and the additional egg yolk, and mix until well combined.
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Add in the vanilla extract, and mix until combined.
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Next, add in the flour, baking soda, salt, and cornstarch. Mix until well combined.
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Lastly, add in the white chocolate chunks and crushed oreos, mixing until combined.
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Cover and chill the dough for 60 minutes (or up to 48 hours).
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Preheat the oven to 350 degrees. Line a large baking sheet with parchment paper.
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With a large cookie scoop, scoop the cookies and cream dough into balls and place evenly spread apart on the baking sheet. (The dough balls should be about 1 - 1 1/2 Tbsp in size.)
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Bake for 12-15 minutes, or until the tops of the cookies have just set.
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Allow to cool on the baking tray for 10 minutes, then transfer the cookies to a cooling rack.
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If desired, while the cookies are cooling, add extra white chocolate and crushed oreos to the tops of the cookies.