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Preheat the oven to 350°F. Lightly grease (or line with parchment) a large baking sheet; an 18” x 13” half-sheet pan is a good choice here.
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To make the dough: In a medium-sized bowl or bowl of your stand mixer, beat together the butter, sugar, salt, and baking powder until the mixture is smooth and creamy.
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Beat in the eggs; the batter may look slightly curdled. With the mixer running at low speed, stir in the flour followed by the bagel topping; the dough will be sticky.
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To shape and bake the dough: Scoop the dough onto the prepared baking sheet. Divide it into two pieces (about 300g each) and shape each piece into a log about 10" x 2" x 3/4" tall.
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Straighten the logs and smooth their tops and sides; a wet spatula or wet bowl scraper works well here. Sprinkle with additional bagel topping, if desired, pressing it in gently.
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Bake the logs for 25 minutes. Remove them from the oven and let them cool on the baking sheet for about 20 minutes, then carefully transfer them to a cutting board.
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Reduce the oven temperature to 325°F.
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To shape and bake the biscotti: 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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Set the biscotti on edge on the prepared baking sheet and return them to the oven. Bake for 25 to 30 minutes, until the biscotti feel very dry and are beginning to turn golden brown.
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Remove the biscotti from the oven and transfer them to a rack to cool.
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Storage information: Store the biscotti in an airtight container at room temperature for several weeks; freeze for longer storage.