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1
In a large mixing bowl or in the bowl of an electric mixer that has a dough hook, blend together the water, yeast, sugar and salt. Stir in the whole egg, the yolk, oil and 1/2 cup honey, and mix well.
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2
Add the 5 cups flour, and mix until the dough is too stiff to mix by hand. Transfer to a lightly floured work surface (if using electric mixer, attach dough hook), and knead to form a soft, supple dough. Add a bit more flour as needed to prevent dough from getting too sticky.
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3
When the dough is smooth and elastic, place it in a lightly oiled bowl, and cover with a sheet of plastic wrap or with a plastic bag. If not using the dough immediately, refrigerate it after it has been kneaded. Bagel making can be resumed up to a day later. Allow the dough to return to room temperature, and continue with step 4.
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4
Let the dough rest about 20 minutes. Punch it down, and divide into 18 equal portions. Pour the water into a Dutch oven, along with the remaining 1/3 cup honey or malt syrup, and heat to boiling. Cover, reduce the heat, and allow to simmer while preparing the bagels.
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5
Shape the dough portions into bagels or doughnutlike rings by elongating each portion into an 8- to 10-inch coil that is 3/4 inch thick. Fold the ends over each other, pressing with the palm of one hand and rolling back and forth gently to seal. This locks the ends together and must be done properly or the bagels will open while being boiled. Let the bagels rest 15 minutes on a towel-lined baking sheet.
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6
Preheat oven to 400 degrees. Bring the water back to a boil and remove the lid. Have bowls of poppy seeds and sesame seeds nearby.
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7
When the water is boiling, use a slotted spoon, and add three bagels to the water. As they rise to the surface, turn them over, and let them boil an additional minute before removing them and quickly dipping them in either bowl of the seeds. Continue boiling the bagels in batches of three until all have been boiled and seeded.
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8
Arrange the boiled bagels on a baking sheet covered with parchment paper or cornmeal, and bake on the lowest rack of oven until they are medium brown, approximately 20-25 minutes. Remove from the oven. Once cooled, the bagels can be placed in a plastic bag, sealed and frozen.
