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Preheat the oven to 350°F with a rack in the center position. Line a baking sheet with parchment or a nonstick baking mat.
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To make the dough: In the bowl of a stand mixer fitted with the flat beater attachment, combine the butter and sugar and beat on medium speed until smooth and fluffy, 2 to 3 minutes. (Alternatively, use an electric hand mixer and large bowl.)
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Scrape the bottom and sides of the bowl. Add the eggs and vanilla and continue beating on medium speed until combined, 2 to 3 minutes. Scrape the bottom and sides of the bowl again, if necessary.
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Add the flour, malted milk powder, cocoa, baking soda, and salt. Mix on low speed until combined, about 1 minute.
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Stir in the chopped chocolate.
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To shape the biscotti: Transfer the dough to a generously floured work surface and press it into a mass. The dough will be very sticky, so feel free to use up to 1/4 cup (30g) flour to dust your surface.
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Divide the dough into two pieces (about 380g each) and form each into a log 10” long and 2” in diameter.
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Transfer both logs to the prepared baking sheet, leaving at least 3” of space between them. Flatten the logs with your hands to about 2 1/2" wide and 3/4" to 1" tall.
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Brush the tops and sides of the logs with the beaten egg and sprinkle with pearl sugar. Transfer the baking sheet to the freezer (no need to cover the logs) and chill for 10 minutes, or for up to 1 hour.
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To bake the biscotti: Once chilled, bake the logs until the tops have lost their sheen and they feel firm when touched, 28 to 32 minutes. Remove them from the oven. Let the logs cool on the baking sheet for 10 minutes, then carefully transfer them to a cutting board.
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Reduce the oven temperature to 300°F.
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Use a serrated knife to cut each log on the diagonal into 3/4"-thick slices. If the biscotti start to crumble, lightly brush or spray the top of the logs with warm water.
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Transfer the biscotti back to the baking sheet, standing them on edge or flat, your choice. Bake until their cut sides feel completely firm and dry, 23 to 25 minutes.
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Remove the biscotti from the oven and let them cool slightly on the baking sheet before transferring to a rack to cool completely.
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Storage information: Store the biscotti in an airtight container at room temperature for up to a week; freeze for longer storage.