In a large bowl, combine 1⅓ cups (320 grams) warm water, yeast, and sugar. Let stand until slightly foamy, 10 to 15 minutes.

Stir olive oil and salt into yeast mixture. Gradually add flour, mixing with your hand. Mix with your hand until dough starts to come together. Turn out onto a heavily floured surface. Knead until dough becomes smooth, 5 to 6 minutes, re-flouring work surface as needed.

Oil a large bowl. Place dough in bowl, cover, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 45 minutes.

Punch down dough. Divide into 8 portions, and shape into rounds. Let stand for 15 minutes.

Heavily flour each portion of dough, and roll or press rounds into 8-inch circles (about ¼ inch thick). Press down firmly with your fingers to create dimples in dough.

Heat a large skillet over medium heat. Add neutral oil to hot skillet. Add 1 dough round, and cook until it starts to puff up, 1 to 2 minutes. Turn, and cook until nicely golden, 1 to 2 minutes. Remove pita from skillet, and place in a clean cotton towel. Repeat with remaining dough. Serve warm, or let cool completely inside towel. Store in a resealable plastic bag for up to 4 days, or freeze in a resealable plastic freezer bag for up to 3 months.