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Combine the water, sugar, barley malt syrup, and salt in a small bowl or measuring cup.
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Stir the mixture to dissolve the syrup and the sugar.
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In a large bowl or mixing bowl of a robust mixer, combine the levain with the bread flour and the water mixture. Clean the levain bowl as you will need it again.
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By hand or using a dough hook, combine the very stiff dough. If you are using a mixer, it may be too stiff to actually knead. Even my Kitchen Aid couldn't handle it for more than a few minutes. The mixer will help combine it and then continue by hand.
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Turn the dough onto a clean work surface.
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Knead the dough for around 10 minutes until it is smooth, springs back when pressed, and in a nice ball. You will probably not need any extra flour as this dough is very stiff. The dough will feel more like pasta dough. It takes some muscle to knead this stubborn dough but be patient. It will smooth out.
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Place the dough back into the bowl you used for the levain.
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Cover the bowl with plastic wrap and let rest for 1 ½ hours. Take the dough out and fold it onto itself into thirds, cupping it around to form a ball again.
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Let rise again until the dough has doubled, around 2 hours more.
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When you are ready to shape the bagels
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Lightly sprinkle some cornmeal or cream of wheat onto the bottom of a baking sheet.
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Divide the dough into 12 equal pieces.
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Roll a piece of dough into a rope around 8 inches or so long. Seal the ends of the rope together by overlapping an inch or two and rolling them together to form a circle. The hole in the middle should be visible but not too large.
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Place the formed bagel onto the prepared baking sheet, thinking about how all 12 will fit on the sheet.
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Continue with the other bagels, rolling, sealing, and placing them evenly on the baking sheet. Keep in mind the bagels will rise.
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Cover the entire baking sheet with plastic wrap or a big plastic bag.
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Let rise for 2 hours. The bagels will have started to puff up but not doubled.
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Place the wrapped baking sheet into the fridge and let retard overnight or between 15 and 24 hours. The longer you retard them, the more sourer they will become.