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Preheat the oven to 375°F. Line two baking sheets with parchment; if you don't have parchment, leave the pan ungreased.
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In a large bowl or the bowl of a stand mixer fitted with the flat beater attachment, beat the peanut butter until totally homogenous, about 1 minute on medium speed.
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Add the butter and beat until no chunks of butter are visible and the mixture is a noticeably lighter color, about 2 minutes on medium speed.
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Add the sugars and beat until light and fluffy.
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Scrape down the sides of the bowl, add the egg, milk, and vanilla, and beat well.
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Mix in the flour, baking soda, and salt on low speed until no dry bits remain. If your dough is sticky or oily, cover the bowl and place in the refrigerater for 30 minutes.
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Shape the dough into 1" balls, then roll them in granulated sugar. (If your dough feels too sticky to roll, transfer it to the refrigerator for 15 minutes to firm up.) Place the balls on the prepared baking sheets, spacing them about 1 1/2" apart.
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Bake the cookies for 10 to 12 minutes, or until they appear set in the center. Remove them from the oven and immediately place one chocolate onto each cookie, pressing gently to adhere.
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Storage instructions: Store peanut butter cookies at room temperature, well-wrapped, for up to a week; freeze for longer storage.