1/2 cup lukewarm water (approximately 80 degrees F)
4 cups bread flour
1 1/2 teaspoon salt
1/4 cup extra virgin olive oil, plus more for greasing
All-purpose flour, for dusting
a pizza peel; a wood-burning pizza oven, optional; a pizza stone, optional
In a stand mixer fitted with the dough hook, combine the yeast, lukewarm water, and 1/2 cup of the bread flour. Mix well and let sit for 30 minutes, or until bubbly like foamy beer.
In a separate medium bowl, whisk together the remaining 3 1/2 cups bread flour and the salt until evenly combined.
Add 3/4 cup cold water and the olive oil to the yeast mixture. Turn on the mixer and begin adding the flour mixture in increments, then mix for 5 minutes, until the dough starts creeping up the dough hook and detaching from the sides of the bowl.
Grease a large bowl with oil and transfer the dough to the bowl. Turn the dough to coat its surface with oil. Cover the bowl loosely with a tea towel. Let the dough rise until doubled in size, about 2 hours. Punch the dough down, then let rise another 1 hour.
Divide the dough into 4 equal pieces and form into discs. On a work surface lightly dusted with flour, use your fingers or the heel of your hands (and a rolling pin, if you prefer) to stretch the discs until they're 13 inches in diameter. The discs should be very thin, less than 1/3 inch.