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Preheat the oven to 350 degrees. Spray a 9-inch square baking pan with cooking spray. Line with foil, allowing several inches of excess to hang over the sides. Spray the foil with cooking spray and set pan aside.
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Cream the peanut butter, butter, and sugar together in a large mixing bowl with an electric mixer until light and fluffy. Beat in the egg, milk, vanilla, baking soda, and salt.
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Turn mixer to low and beat into the flour until just combined. Fold in the peanut butter cups with a rubber spatula
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Press into an even layer in the prepared pan and bake 20 to 25 minutes, until puffed and golden around the edges.
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Remove from the oven set pan on a wire rack to cool room temperature. Once the bars have cooled, use the foil to remove the bars from the pan, then slice and serve.
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Uneaten cookie bars can be stored in an airtight container at room temp for up to 2 days or in the freezer for up to 3 months.