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For the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine all of the ingredients except the burnt sugar syrup and cocoa in a large bowl and mix well. If you'd like to use a bread machine to make the dough, see baker's tips below.
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Once the dough comes together, knead vigorously for 10 to 15 minutes by hand or in a mixer with a dough hook on medium-low speed for 10 minutes. The dough will be stiff.
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Divide the dough in half; place one half in a lightly greased bowl, cover, and set aside.
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Add the burnt sugar syrup to the remaining dough in the mixing bowl. Mix until it disappears into the dough; this will be messy at first, but everything will smooth out in a few minutes.
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Add the black cocoa and mix until incorporated. Knead the dough until it's dark and evenly colored. Place the colored dough in another greased bowl and cover.
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Let the doughs rise until noticeably puffy, 1 to 1 1/2 hours.
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After the first rise, pat the light dough into an 8" x 12" rectangle. Pat the colored dough to the same size and place it on top.
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Divide the dough into quarters by cutting it crosswise to make 2"-wide strips. Cut in half the long way to make eight equal pieces.
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Roll each two-toned piece of dough into a 7" to 8" rope. Twist two or three times and overlap the ends, wetting one slightly if needed. Roll your hand over the seam from the inside of the bagel to seal it.
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Line two baking sheets with parchment and space out the shaped bagels on the pans. Cover and let rise for 20 minutes while you set up the water bath and preheat the oven to 450°F.
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To boil: Fill a large saucepan with the water (it should reach a depth of about 3"). Add the malt powder (or brown sugar) and granulated sugar and place the pan over medium-high heat. Bring the water to a boil.
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The bagels are ready to cook when they've risen very slightly; they should still be firm enough that the surface bounces back when lightly touched.
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Reduce the heat under the water to medium (a slow bubble) and slip two or three bagels into the water. Cook for 1 minute, then turn over and cook for 2 more minutes.
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Remove the bagels from the water with a slotted spoon and place on the prepared baking sheets.
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For the egg wash: Beat the egg whites with the water.
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Brush the tops of the bagels with the egg wash, and bake for 20 to 22 minutes, until golden brown.
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Remove the bagels from the oven and let cool on a rack before serving.
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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.