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To make the preferment: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Mix the preferment ingredients in a small bowl, cover, and let rest at room temperature overnight.
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To make the dough: Combine the preferment and the remainder of the dough ingredients, and mix and knead by hand, or using a stand mixer, to make a smooth dough. It won't be particularly soft nor stiff; it should be smooth and feel bouncy and elastic under your hands.
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Place the dough in a lightly greased bowl or other container. Cover it, and let it rise at room temperature until it's very puffy, about 1 1/2 hours, turning it over and gently deflating it after 45 minutes.
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To shape the sub rolls: Turn the dough out onto a lightly oiled work surface. Divide it into six pieces.
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Roll the pieces into cylinders, 4 1/2" in length. Flatten the cylinders slightly; dough rises more in the center, so this will give a gently rounded top versus a high top.
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Place the loaves on a lightly greased or parchment-lined baking sheet. Cover and let rise until almost doubled, about 45 minutes. While they're rising, preheat the oven to 425°F.
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Brush the rolls with the egg white mixture. If you like a classic look, slash diagonally several times (as you'd do with a baguette); or make one long slash the length of the roll. Bake for 20 to 25 minutes, or until the internal temperature reaches 190°F.
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Remove the rolls from the oven and transfer them to a rack to cool.
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Storage information: Store leftover Italian Sub Rolls, well wrapped, at room temperature for several days; freeze for longer storage.
