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In a large bowl, stir together the water, barley malt syrup, yeast, and 1 cup of flour. Cover and let work for about 10 minutes, until the mixture is bubbly.
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Stir in the salt and an additional 2 1/4 cups of flour, adding the remaining 3/4 cup of flour if the dough is too sticky.
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Mix until the dough comes together and begins to pull away from the sides of the bowl.
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Turn out onto a well-floured work surface. Knead for 3 to 4 minutes, then cover and let rest while you clean and grease the mixing bowl.
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Knead for 3 to 4 minutes more, until the dough is smooth, elastic, and no longer sticky. If adding a flavor (see tips below), add it at this point.
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Place the dough in the bowl and cover. Let rise until almost doubled in bulk, about 1 1/2 hours.
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Gently deflate the risen dough and roll it out to about 1/2" thick on a floured surface.
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Choose a method to form your bagels from the techniques below and place them on lightly floured parchment to rest (about 15 minutes) while you preheat the oven to 450°F.
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Method I: Portion the dough into 8 equal pieces and round each into a ball. Stick your finger through the center of the dough ball and twirl the dough around your finger until the center is about 1 1/2" in diameter.
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Method II: Use a doughnut cutter, or a 3" round cutter for the circle and a 1/2" round cutter to cut out the center. Pull the hole open a little larger before boiling.
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Method III: Portion the dough into 8 equal balls (2 5/8 ounces each) and roll into a log about 6" long. Wet the ends and overlap them. Flour your fingers and put them through the center of the bagel; roll them over the dough where it overlaps to seal it.
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To boil: Placed the water in a large saucepan. Add the malt syrup for shiny bagels (or the salt for a salty exterior). Place the pan over medium-high heat and bring the water to a boil.
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The bagels are ready to cook when they've risen slightly (they should still be firm enough that the surface will bounce back a bit when lightly touched).
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Reduce the heat to medium and slip 2 or 3 bagels into the water.
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Cook for 1 minute, then turn over and cook for 2 more minutes more.
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Remove from the water with a slotted spoon and return to the baking sheets.
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Brush the tops with egg wash, and sprinkle with the garnish of your choice (see baker's tips below).
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Bake for 18 to 20 minutes, until golden brown.
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Remove from the oven and let cool on a rack.
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Store in a paper bag on the counter for one day; or slice and freeze for up to two months for longer storage.