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Preheat the oven to 400°.
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Line baking sheets with Silpats or parchment paper; set aside.
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In a small bowl, sift together flour, baking powder, and salt; set aside.
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In a heatproof bowl or the top of a double boiler set over a pot of simmering water, melt together the unsweetened and semisweet chocolates and the butter; set aside to cool.
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In the bowl of an electric mixer fitted with the whisk attachment, beat eggs, sugar, and vanilla on medium speed until light and fluffy, about 3 minutes.
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Add cooled, melted chocolate mixture, and combine on low speed.
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Add flour mixture, and continue to beat on low speed until almost combined, about 1 minute.
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Remove bowl from mixer; stir in milk chocolate by hand.
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Using a 1/2-ounce ice-cream scoop, drop dough onto prepared baking sheets about 3 inches apart.
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Bake until set, 12 to 15 minutes.
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Let cookies cool completely on baking sheets.