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Whisk together yeast, 2 Tbsp flour, and 1/2 cup warm water in a measuring cup and let stand until mixture develops a creamy foam, about 10 minutes. (If mixture doesn’t foam, discard and start over with new yeast.)
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Stir together salt and 3 cups flour in a large bowl. Add yeast mixture and remaining 1 1/2 cups warm water and stir until smooth, then stir in 1 cup more flour. If dough sticks to your fingers, stir in just enough flour (up to 3/4 cup), a little at a time, to make dough just come away from side of bowl. (This dough may be wetter than other pizza doughs you have made.)
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Knead dough on a lightly floured surface with floured hands, lightly reflouring work surface and your hands when dough becomes too sticky, until dough is smooth, soft, and elastic, about 10 minutes.
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Divide dough in half and form into 2 balls, then generously dust balls all over with flour and put each in a medium bowl. Cover bowls with plastic wrap and let dough rise in a draft-free place at warm room temperature until doubled, 1 to 1 1/4 hours.
