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To make the starter: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine all of the ingredients and mix until uniform. Cover and let rest at cool room temperature overnight.
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To make the dough: Combine the starter with the remaining ingredients to form a stiff dough. Knead by hand for 12 minutes, or in a mixer for 9 minutes. The dough will be smooth and elastic, and should not spread much when you stop kneading.
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Place the dough in a lightly greased bowl, and let rise until puffy but not necessarily doubled in bulk, 1 to 1 1/2 hours. After this rise, transfer the dough to a clean work surface, gently deflating it in the process.
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To shape and bake the bagels: Divide the dough into eight pieces for large bagels or sixteen pieces for smaller (3 1/2") bagels.
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Roll each piece into a ball, cover, and let rest for 30 minutes. They'll puff up very slightly.
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Poke a hole through the center of each ball, then twirl it around on your finger until the hole is 1 1/2" in diameter.
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Place the shaped bagels on a lightly greased or parchment-lined baking sheet, and allow to rise, covered, for about 45 minutes.
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While the bagels are rising, place a steamer rack in a wide pan or canning kettle. Put 1" to 2" of water in the bottom and bring it to a simmer.
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Preheat the oven to 400°F.
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Place as many bagels as will fit on the steamer with 3/4" of space between them. Cover the pan and steam the bagels for 90 seconds.
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Using a spatula and your fingers, gently remove the bagels from the steam and return them to the baking sheets. Repeat until all of the bagels are steamed.
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If you wish to top the bagels with seeds or other toppings, brush with beaten egg wash, and apply the seeds of your choice.
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Bake the bagels for 20 to 25 minutes, or until deep golden brown.
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Remove the bagels from the oven, and let cool on a rack.
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Homemade bagels are best stored in a paper bag on the counter for 1 day; or slice and freeze for up to 2 months for longer storage.