In a large mixing bowl, whisk together flour and salt. Create a well in the center and pour in warm water, olive oil, and vinegar. Mix with a fork until shaggy, then knead by hand for 8-10 minutes until smooth and elastic.

Form the dough into a ball, lightly coat with olive oil, wrap in plastic, and let rest at room temperature for at least 1 hour (or up to 2 hours).

Dust a large, clean surface with flour. Have additional flour and cornstarch nearby for dusting as you work.

Cut the dough into 8 equal portions. Keep pieces covered with a slightly damp towel to prevent drying while you work with one piece at a time.

Working with one piece, shape it into a disc and dust lightly with flour. Using a rolling pin, roll it into a thin circle, rotating frequently and dusting with flour as needed to prevent sticking.

Once you've rolled the dough as thin as possible with the rolling pin (about 12 inches in diameter), gently lift it onto the backs of your hands and carefully stretch it from underneath, working in a circular motion.

Place each sheet on a clean, lightly floured surface. Dust lightly with cornstarch before stacking the next sheet on top. Continue until all dough pieces are stretched.

Fresh phyllo is best used right away, but you can store the sheets by layering them between pieces of parchment paper, wrapping tightly in plastic, and refrigerating for up to 2 days.