Italian Sub Rolls

To make the starter: Mix the starter ingredients in a small bowl, cover, and let rest at room temperature overnight., Combine the starter 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., 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 90 minutes, turning it over and gently deflating it after 45 minutes., Turn the dough out onto a lightly oiled work surface. Divide it into six pieces., 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., 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., Brush the rolls with the egg white mixture. Bake for 20 to 25 minutes, or until the internal temperature reaches 190°F., Remove the rolls from the oven and transfer them to a rack to cool. Store, well-wrapped, at room temperature for several days; freeze for longer storage.