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To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.
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In the bowl of a stand mixer fitted with the dough hook, combine the dough ingredients. Mix and knead at medium speed until a strong, smooth, elastic dough forms. The dough will stick to the bottom of the bowl at first but will form a ball as it develops. It’s ready when you can stretch a small piece of it thin enough, without tearing, to see through (the "windowpane test"), which can require up to 15 minutes of kneading.
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Form the dough into a ball, place it in a covered bowl or dough-rising bucket, and let it rest in a warm place (76°F to 78°F is ideal) for 1 1/2 to 2 hours.
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To make the sauce: While the dough is rising, use a blender or food processor to purée the tomatoes, olive oil, garlic, sugar, salt, and pepper until smooth.
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Transfer the tomato mixture to a medium saucepan set over medium-high heat. Add the basil.
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Bring the tomato mixture to a gentle simmer then lower the heat and cook, stirring regularly, until the mixture has thickened to a tomato sauce-like consistency, about 10 to 15 minutes.
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Remove the sauce from the heat and pour it into a heat-safe measuring cup; you should have about a cup of sauce. Set it aside.
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Toward the end of the dough’s rise, preheat the oven to 450°F. Coat the inside of a 9” x 5” loaf pan with olive oil.
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To shape the scaccia: Transfer the dough to a greased work surface that’s about 24” x 30” in area.
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Roll the dough into a very thin rectangle about 18" x 24” in size; it should be thin enough to see through it in places. If the dough resists stretching, cover it and let it rest for 10 minutes or so, to relax.
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Lightly score the dough into 18” x 6” quarters; don’t cut all the way through, just mark it.
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Spread about 1/2 cup of the tomato sauce evenly over the center two quarters and sprinkle half the cheese atop the sauce.
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Fold the two uncovered sections on either side into the center, overlapping them slightly where they meet. You’ll now have a rectangle that’s about 18” x 12”.
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Lightly score the dough into four 4 1/2" x 12” sections. Spread a scant 1/3 cup of the remaining tomato sauce evenly over the center two sections and top with three-quarters of the remaining cheese.
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Fold the two uncovered sections into the center, overlapping them slightly where they meet. You’ll now have a rectangle that’s about 9” x 12”.
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Lightly score the dough into three 9” x 4” sections. Spread the remaining sauce over the left two sections and top with the remaining cheese.
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Fold the right (un-sauced) section over the center section and then fold the left (sauce-covered) section over both, like you'd fold a letter.
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Transfer the loaf seam-side up to the prepared pan and pierce the top with a fork about a dozen times.
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Bake the loaf for 50 to 60 minutes, until the top is dark and blistered in places; a digital thermometer inserted into the center of the loaf will read 212°F.
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Remove the loaf from the oven and turn it out of the pan onto a rack.
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Allow the scaccia to cool slightly (for about 10 minutes) before cutting it into thick slices. Serve warm or at room temperature.
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Store leftover scaccia, well wrapped, for 2 to 3 days at room temperature; freeze for longer storage. Toast slices or reheat to serve.