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Preheat the oven to 350 degrees.
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Whisk together the flour, cocoa powder, baking soda, and salt in a medium bowl. Set aside. (These are your dry ingredients.)
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Combine the butter and granulated sugar in a large bowl and beat with an electric mixer on medium until light and fluffy. Add the milk, egg, and vanilla, and beat to combine.
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With mixer on low, beat in the dry ingredients until incorporated. Use a rubber spatula to stir the dough a few times to ensure everything is well combined.
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Drop heaping tablespoons 2 inches apart onto ungreased, unlined baking sheets and bake for 8 minutes.
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Remove the baking sheets from the oven, press a marshmallow half (cut-side down) onto the top of each cookie. Return the baking sheets to the oven for 2 minutes more.
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Remove from the oven and press the marshmallows down lightly with your hand to make a flat surface for the frosting. Carefully transfer the cookies to wire racks to cool completely before you frost them.