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In a large bowl or the bowl of a stand mixer, combine all the dough ingredients. Mix using a spoon (if mixing by hand) or the flat beater attachment (if using a stand mixer) until a sticky, batter-like dough forms, about 1 minute on medium speed. If mixing by hand, there may be some lumps — that's OK. It’s normal for the mixture to resemble cake batter at this stage.
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Cover the mixture and set aside for 20 minutes. It will begin to firm up slightly during this time and look more like dough than batter. Then, on a greased or (gluten-free) floured work surface, gently knead the dough — fold the dough in half towards you (use a bowl scraper for assistance, if needed), then pat it down, rotate the dough 90° (a quarter turn) and fold again — until it becomes firmer to the touch, smoother, and easier to handle, 5 to 6 times. As you work, dust your work surface and the dough lightly with gluten-free flour (or apply more grease) as needed to prevent sticking. The dough may still be sticky to the touch but should have some bounce and body by the end of kneading.
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Return the dough to the mixing bowl, cover, and allow it to rise for 40 minutes, or until slightly puffy.
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In a medium bowl, combine all the filling ingredients except the chocolate and nuts. Stir until a very soft paste is formed. Set aside.
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On a greased or floured surface, gently deflate the dough and pat or roll into an 8" x 16" rectangle. Don’t worry if it isn’t perfectly 16" long. The dough will feel soft and spongy at this point.
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Use a small offset spatula or the back of a spoon to spread the chocolate filling evenly over the dough leaving a 1" border bare on every side. Scatter the chocolate and nuts over the surface evenly.
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Starting on a short side, roll the dough gently into an 8" to 9" log, then pinch the seam and ends closed to seal the filling inside.
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Use a serrated knife or kitchen scissors to cut the log in half lengthwise to make two pieces of dough, each about 9" long; cut carefully to prevent too much filling from spilling out. With the exposed filling side up, gently twist the two pieces together, tucking the ends underneath. It’s OK if one or two of the now-exposed inner dough coils tears slightly at this point. Place the log into a lightly greased 8 1/2" x 4 1/2" loaf pan.
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Brush loaf with egg wash (reserve any excess), cover, and allow it to rise for 30 to 45 minutes, or until the loaf is puffy and has risen above the edge of the pan by about 1" in the center.
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While your dough is rising, preheat your oven to 350°F.
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Before baking, brush the gluten-free babka with the egg wash once more.
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Bake the gluten-free babka for 30 minutes, then tent with foil and continue baking for 25 to 30 minutes, or until the babka is a deep golden brown. To ensure the loaf is baked through, insert a digital thermometer into the center of the loaf. It should register at least 190°F when it’s done.
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Remove the gluten-free babka from the oven and immediately loosen the edges with a heatproof spatula or table knife. Let the babka cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely. Slice and serve at room temperature.
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Storage information: Store any leftover gluten-free babka, well wrapped, at room temperature for up to 2 days. After 2 days, rewarm individual slices briefly in a toaster, if desired. Freeze for longer storage.