Make sponge: In a large bowl, mix yeast with 2 cups warm water (105° to 115°), sugar, and bread flour with a wooden spoon until smooth. Cover with plastic wrap and let rest in a warm place (80° to 90° is ideal) overnight.
Lightly oil a large bowl and set aside. In a stand mixer fitted with the dough hook, combine sponge, 1 cup warm water, all-purpose flour, 3 cups bread flour, and salt. Mix at low speed until dough is soft, sticky, and smooth, 6 to 8 minutes.
Increase speed to medium and gradually sprinkle in remaining 1 cup bread flour. Mix until smooth, then cover bowl with a kitchen towel and let rest 30 minutes.
Mix dough at low speed a couple of minutes, or until it begins to pull away from the sides of the bowl. If it doesn't, let it rest another 15 minutes; then mix again.
Turn dough out onto a floured work surface and sprinkle with flour. With floured hands, knead dough several times until smooth and slam the dough hard onto surface a few times to help the gluten develop and make dough more elastic.
Put dough in oiled bowl, cover tightly with plastic wrap, and let rise at room temperature until doubled in volume, 2 to 4 hours. Divide into 10 equal portions and roll each into a tight ball.
Let balls rise about 20 minutes covered with a kitchen towel. They are ready to use now, but if you want to store them, put them side by side in a lightly oiled 9-by-11-by-2-in. container with a lid. Drizzle tops with oil to keep a skin from forming.
*Make ahead: Chill in container overnight or freeze up to 6 months. Let dough come to room temperature before proceeding.
Note: Nutritional analysis is per dough ball.