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To make the dough: Use your fingers to rub together the sugar and lemon zest until all of the sugar is moistened. Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine the lemon sugar with the flour and yeast in the bowl of a stand mixer fitted with the beater blade. Mix on low speed to combine, about 1 minute.
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Add the eggs, water, and salt, and mix on low speed briefly. Increase to medium speed and mix for 5 minutes, until the dough comes together (it will appear very dry and shaggy at first; that’s OK).
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Switch to the dough hook. Add the butter a few cubes at a time, kneading until each cube is completely incorporated into the dough. Continue kneading on medium speed for about 10 minutes, until the dough is completely smooth, elastic, and shiny.
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Place the dough in a large greased bowl, turning to coat it, and cover with plastic wrap. Refrigerate overnight.
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To make the filling: Place the chocolate, butter, and cocoa powder into a medium heat-proof bowl and microwave in 30-second increments until the chocolate is completely melted, stirring after each (it will take around 2 minutes).
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Add the confectioners’ sugar, mixing until thoroughly incorporated. Set aside to thicken, about 30 minutes; the mixture should be malleable, the consistency of soft ganache.
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To assemble the babka: Divide the dough in half. Working with one piece at a time, roll the dough on a lightly floured surface into a 15” x 11” rectangle.
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Use an offset spatula to spread half the chocolate mixture over the dough, leaving a 1/2” border around the edges. Brush a little bit of water along the long edge of the rectangle farthest away from you.
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Starting from the long side closest to you, roll the dough into a log. Press to seal the dampened end, then use both hands to even out the roll. Rest the log on its seam.
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Trim about 3/4” off each end of the roll using a serrated knife. Using the same knife, gently cut the roll in half lengthwise, starting at the top and finishing at the seam underneath.
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With the cut sides facing up, gently alternate crossing the pieces over each other to create a two-strand braid.
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Repeat with the second piece of dough and remaining chocolate filling.
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Line a large baking sheet with parchment paper. Gently transfer the two babka braids to the prepared pan and shape them into one large circle, braiding together the ends for continuity.
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Cover with lightly greased plastic wrap and allow to rise in a warm place for 1 1/2 hours; the babka won’t double in size, but will rise by about 20 percent. Towards the end of the rising time, preheat the oven to 375°F.
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Remove the plastic wrap. Bake the babka for 25 to 30 minutes, until a skewer inserted into the center of the dough comes out clean and all of the exposed chocolate swirls are firm to the touch.
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While the babka is baking, make the glaze. Combine the water and sugar in a small saucepan and bring to a boil over medium heat. When the sugar is fully dissolved, remove from the heat and set aside.
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As soon as the babka comes out of the oven, brush all of the glaze over the babka; it will seem like a lot, but just keep brushing!
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Slide the parchment paper from the baking pan to a cooling rack. Allow the babka to cool completely before serving.
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Store any leftovers, well wrapped in plastic, at room temperature for up to 3 days; freeze for up to a month.
