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Preheat oven to 350 F. Line two baking sheets with parchment paper. Set aside.
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In a medium bowl, sift together flour, baking powder, baking soda, and salt. Set aside.
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Beat butter in a large bowl. Add sugar and cocoa powder and beat until combined, about 3 minutes.
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Add the eggs and vanilla and beat until combined.
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On a low speed, alternately add the flour mixture and the milk in three additions, starting and ending with the flour. Mix until combined.
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Scoop about two tablespoons worth of dough onto prepared baking sheet. Flatten into a 2-inch circle using an offset spatula. Leave a couple inches of space between each cookie as they will expand while baking.
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Bake cookies for 12 minutes, until the edges of the cookies are set. Let cookies cool for 2 minutes on the baking sheet before transferring to a wire rack. It might be necessary to replace the sheets of parchment on the baking sheets between batches of cookies.
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Let the cookies cool completely before frosting.