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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.
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To make the dough: In a large bowl or bowl of a stand mixer, combine all of the dough ingredients (starting with the lesser amount of water), mixing until everything is moistened. Add additional water if necessary to enable the dough to come together. Cover the bowl, and let the dough rest for 20 minutes. Then mix/knead it until it's soft and smooth.
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Place the dough in a lightly greased bowl, and cover the bowl. The dough is going to rise for about 1 1/2 to 2 hours, until it's quite puffy.
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Gently deflate the dough, and divide it in half. Set the pieces aside, covered, while you make the filling.
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To make the filling: Combine the sugar, cinnamon, cocoa, and espresso. Stir in the melted butter. The mixture will look grainy and slick; that's OK.
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Shape each half of the dough into a 9" x 18", 1/4"-thick rectangle. If the dough "fights back," let it rest for 10 minutes to relax the gluten, then stretch it some more. Don't be fussy about this; 19" or 20" is as good as 18".
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Smear each piece of the dough with half the filling, coming to within an inch of the edges.
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Scatter half the nuts, and half the chopped chocolate/chips over each piece. If using standard-size chips, process them in a food processor first, to create smaller bits of chocolate and a less chunky filling.
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Starting with a short end, roll each piece gently into a log, sealing the seam and ends. Working with one log at a time, use a pair of scissors or a sharp knife to cut the log in half lengthwise (not crosswise) to make two pieces of dough about 10" long each; cut carefully, to prevent too much filling from spilling out. With the exposed filling side up, twist the two pieces into a braid, tucking the ends underneath. Repeat with the other log. Place each log into a lightly greased 9" x 5" loaf pan.
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Brush each loaf with the egg glaze. Mix together the topping ingredients until crumbly, and sprinkle half the topping over each loaf.
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Tent each pan with plastic wrap, and let the loaves rise until they're very puffy and have crowned a good inch over the rim of the pan, 1 1/2 to 2 1/2 hours. Towards the end of the rising time, preheat your oven to 300°F.
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Bake the bread for 35 minutes. Tent lightly with foil, and bake for an additional 15 to 25 minutes (for a total of 50 to 60 minutes); the loaves should be a deep-golden brown.
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To ensure the loaves are baked through, insert a digital thermometer into the center of one loaf. It should register at least 190°F.
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Remove the loaves from the oven, and immediately loosen the edges with a heatproof spatula or table knife. Let the loaves cool for 10 minutes, then turn them out of the pans onto a rack to cool completely.
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Serving and storage information: Slice the babka and serve it at room temperature; or rewarm individual slices briefly in a toaster, if desired. Store any leftovers, well wrapped, at room temperature for several days; freeze for longer storage.