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To make the starter: Mix the starter ingredients in a small bowl until well combined. Cover the starter and let it rest at room temperature overnight, or for up to 15 hours. It will become bubbly.
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Place all of the dough ingredients, including the starter, into the bowl of your mixer, and beat at medium speed, using the flat beater, for 7 minutes. The dough will be very smooth, soft, shiny, and elastic. Alternatively, knead the dough ingredients in your bread machine using the dough cycle.
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Transfer the dough to a greased bowl or other rising container, cover it, and let it rise for 2 hours. Give the dough a fold: Turn it out onto a floured surface and, using a bowl scraper or bench knife, fold it like a business letter. Turn the dough 90 degrees. Gently flatten it a bit, and repeat the letter fold. Return the dough to the bowl, cover, and let it rise for another hour. Note: If you're using a bread machine, simply allow it to rise for an additional hour after the dough cycle has ended; there's no need to take it out and give it a fold.
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Lightly grease your work surface, and two half-sheet baking pans (18" x 13") or similar large baking sheets. Grease your hands, as well.
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Turn the dough out of the bowl onto a lightly greased work surface.
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Pat the dough into an 8" x 10" rectangle and cut it into 12 squares (about 2 1/2" each).
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Transfer the rolls to the baking sheets, leaving about 3" between them.
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Lightly cover the rolls with heavily oiled plastic wrap or a proof cover, and allow them to rise for 2 to 3 hours, or until they're showing some signs of puffiness. Towards the end of the rising time, preheat the oven to 425°F.
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Spritz the risen rolls with lukewarm water, and gently but firmly dimple each one with your fingers, making fairly deep pockets. Note: For extra-crusty crust, forgo spritzing the rolls with water and instead add steam to your oven; for details see "tips," below.
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Immediately place the rolls into the oven. Bake them until they're golden brown, about 18 to 20 minutes. Remove them from the oven, and cool on a rack.
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Slice crosswise, and add your favorite fillings. Store any leftovers, tightly wrapped, at room temperature. Rolls may be reheated just before serving, if desired; tent lightly with foil, and heat for about 8 minutes in a 350°F oven.