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Preheat the oven to 350 degrees. Spray an 9-inch square baking pan with cooking spray and set aside.
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Combine the cream cheese, sweetened condensed milk, egg, vanilla, and salt in a large mixing bowl. Beat with an electric mixer set to medium speed until very smooth and creamy, about 3 minutes. Fold in the chopped peanut butter cups.
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Press two-thirds to three-quarters of the cookie dough into the bottom of the prepared pans—enough to cover the bottom in an even layer. Pour the cheesecake mixture evenly over the cookie layer and smooth the top with a rubber spatula. Break up remaining cookie dough into small pieces and sprinkle over the cheesecake layer.
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Bake until slightly browned on top, 30 to 35 minutes. Set pan on a wire rack and cool fully.