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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 sponge: In a large mixing bowl or the bowl of your stand mixer, stir together the sponge ingredients. Cover loosely with plastic wrap, and set aside to proof for 10 to 15 minutes.
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To make the dough: In the same bowl, combine the sponge with the yogurt, butter, eggs, sugar, salt, and vanilla. Add 4 1/2 cups (540g) of the flour and mix with the paddle attachment until the dough is a rough, shaggy mass.
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Switch to the dough hook and knead on speed 2 until a soft, smooth dough forms, about 5 to 6 minutes. Add more flour, if necessary, to achieve the correct consistency.
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Place the kneaded dough in a lightly greased bowl, cover with plastic wrap, and allow it to rise until it's quite puffy and nearly doubled, about 60 to 90 minutes. While the dough is rising, prepare the filling.
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To prepare the filling: Combine all the filling ingredients (except the lemon curd) in a small bowl, mixing until smooth and lump-free. Reserve the filling and lemon curd until ready to fill the braids.
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Gently deflate the dough and divide it in half. Cover half with plastic wrap and set it aside as you roll the first piece into a 10" x 15" rectangle. Rolling on parchment paper makes moving the bread to the baking sheet much easier.
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Lightly press two lines down the dough lengthwise, to visually divide it into three equal sections. Spread half the cream cheese filling down the center section and top with half the lemon curd, leaving 1" bare of filling at each end of the dough.
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To shape the braid: Begin by using your bench knife, a pair of scissors, or a sharp knife to cut and remove a 1” rectangle from each of the dough's four corners. This “notching” will make the ends of the finished braid neater.
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Next, fold the resulting dough "tab" over the edge of the filling on one end. Starting at that same end, cut 1" crosswise strips down the length of the outside sections, making sure you have the same number of strips on each side.
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Beginning on the left, lift the top dough strip and gently bring it across the filling diagonally. Repeat on the other side with the top dough strip, so that the two strips crisscross each other. Continue down the entire braid, alternating strips to form the loaf. When there are just two strips remaining (one on each side), fold the remaining "tab" over the filling, then crisscross the final two strips.
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Repeat the rolling, filling, and braiding steps for the second piece of dough, using the remaining cream cheese filling and lemon curd. Set both loaves aside, lightly covered, to rise until quite puffy, 45 to 50 minutes.
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Preheat the oven to 375°F. Brush the loaves with the beaten egg, and sprinkle with pearl sugar or coarse sparkling sugar.
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To bake the braids: Uncover the braids and bake them for 25 to 30 minutes, or until they're golden brown. Remove them from the oven and cool for 15 to 20 minutes before serving.
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Store any leftovers, well wrapped, in the refrigerator for a couple of days; freeze for longer storage. Reheat (or thaw and reheat) briefly before enjoying.