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To make the rye sourdough: In a medium bowl combine the water and sourdough starter, breaking up the sourdough with your fingers or a spatula to distribute it. Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Add the flour, stirring until everything is well combined.
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Cover the sourdough and set it aside at room temperature for 12 to 16 hours.
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To make the final dough: In a large bowl, combine the prepared sourdough with the water. Mix with your hands, a spoon, or a spatula until the sourdough is broken up in the water.
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Add the remaining ingredients and stir until they’re fully incorporated. The shaggy dough will be more like a thick batter; a plastic dough scraper is a handy tool for incorporating everything from the bottom and sides of the bowl.
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Scrape down the sides of the bowl and allow the dough to rise, covered, until it’s domed and slightly puffy, about 1 hour at room temperature; the dough will not double in size.
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Transfer the dough to a lightly floured work surface and divide it in half. If you have a scale, each piece will weigh about 800g.
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Shape each piece of dough into a round (boule) and place them upside down into flour-dusted bannetons (brotforms) or towel-lined bowls about 8" in diameter. Let the loaves rest, covered, for 30 minutes.
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While the loaves are resting, preheat the oven to 450°F with a baking stone in the middle and an oven-safe pan on the bottom rack or oven floor.
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Transfer the loaves to a piece of parchment paper large enough to fit them but not larger than your baking stone.
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Let the loaves rest, uncovered, until small cracks begin to appear on the surface, another 10 to 15 minutes or so.
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With 1 cup of hot water at the ready, transfer the loaves on the parchment to the hot baking stone. Pour the hot water into the pan below, and immediately close the oven door to trap the steam.
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Bake the loaves for 45 to 50 minutes, until they’re well colored; a digital thermometer inserted into the center of a loaf will read 210°F.
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Turn off the oven, leaving the loaves inside but propping the oven door open a few inches, to allow the bread to set for another 10 minutes.
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Remove the loaves from the oven and transfer them to a rack to cool completely before slicing.
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Store leftover bread, in paper bags or wrapped in a tea towel, at room temperature for up to a week. Freeze for longer storage.