Mix water and yeast in a large bowl and let stand 5 minutes to proof. Gradually pour in 2 cups of the flour and stir to incorporate. Mix for about 1 minute to form a sponge. Let stand, covered, for at least 1 hour.
Put sponge in the bowl of a stand mixer. Using the dough hook, add the salt and oil, then add the flour, 1/2 cup at a time, to form a dough. Remove from bowl and knead. Place in a clean oiled bowl and let rise, slowly, about 2 1/2 hours. Divide dough into 4 balls, let rise again for 1/2 hour, and then roll out as desired.