In a large bowl, combine the yeast, sugar, and water. Let sit for about 5-10 minutes, or until the mixture begins to foam and bubble.
Whisk in the yogurt, olive oil, and salt. With a wooden spoon, gradually mix a floor and parsley. Turn the dough onto a generously floured surface and knead for 3-4 minutes until no longer sticky and/or springs back when lightly pressed.
Divide the dough into 10 equal balls. Sprinkle lightly with flour and cover the dough with a clean kitchen towel. Let rest for 15 minutes.
Preheat a medium sauté pan over medium-low heat. Using a rolling pin or your hands, roll or stretch each piece of dough into a large circle, about 6-8 inches across. Repeat with the remaining dough. Brush the top of each lightly with olive oil.
Once the pan is hot, place the dough, oil side down. Lightly brush the top surface with olive oil. Allow the flatbread to cook for 1-2 minutes, until bubbles form and the under side is spotted with gold. Flip and cook for another 1-2 minutes, careful not to burn. Stack flatbreads in a clean kitchen towel to retain moisture while repeating the cooking process with the remaining dough.
Top finished flatbreads with chopped fresh parsley. Use as an accompaniment to any meal or soup.