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Preheat oven to 325 degrees and place rack in center of oven.
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Cream butter, sugars and peanut butter until smooth on medium speed.
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Add eggs and vanilla and beat until smooth on medium speed.
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Turn off mixer and add flour, oats, salt and baking soda to bowl. Pulse mixer or mix on low until ingredients are incorporated. I pulse the ingredients, then use a large silicone spatula to scrape the bottom of the bowl and fold until the ingredients are all mixed together.
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Bake for 18-20 minutes for 9x13 or about 20-25 minutes for 11x18 jelly roll pan.
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Remove from oven and turn heat off. Sprinkle chocolate chips onto top of cookie layer.
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Return to oven for 2 minutes. Remove pan again and using a knife or offset spatula, spread melted chocolate chips evenly over cookie layer.
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Let cool completely on counter, or place in fridge to speed up cooling process (see recipe notes).
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Make peanut butter frosting by creaming softened butter and peanut butter together in a large bowl. Add powdered sugar, dash of salt and milk until light and fluffy. Spread on top of cooled chocolate mixture.
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Cut into pieces and serve.