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Whisk together 1 cup bread flour, cornmeal, yeast, 2 tablespoons sugar, and salt in the bowl of a stand mixer.
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Heat water to warm (120° to 130°F) and add it and the oil to flour mixture. Stir to combine. Add egg and stir to combine.
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Blend on medium speed using the flat beater for 3 minutes. Switch flat beater to dough hook and turn mixer to the manufacturer's recommended speed when using a dough hook.
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Whisk together remaining flours and gradually add enough to make a soft dough and the dough "cleans" the sides of the bowl. Knead with dough hook for 4 minutes.
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Hand knead dough a few times until smooth. Place in a greased bowl, turning to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
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Heat oven to 375°F. Line rimmed baking sheets with parchment paper.
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Bring a large pot of water 3-inches deep to a low boil (or fast simmer) and add 1 tablespoon of sugar for every quart of water.
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Punch down dough and divide it into 12 equal pieces.
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Shape each piece into a smooth ball. Use a finger to punch a hole in the center. Gently pull dough to make a 1- to 2-inch hole.
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Place a few bagels at a time in the boiling water (bottom side up works best). Turn bagels over after 45 seconds. Boil for another 45 seconds then remove bagels from water using a slotted spoon and place them on a wire rack to drain for a few minutes.
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Place drained bagels on baking sheets.
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If you want to top the bagels with seeds, brush tops with beaten egg white and sprinkle the seeds on top.
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Bake bagels until golden brown, about 20 to 25 minutes. Rotate sheets half way through baking for even browning.
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Transfer bagels to a wire rack to cool completely.