Combine the yeast, sugar, and water into a medium-large bowl and stir well.
Then mix in your greek yogurt and olive oil.

Add the flour, salt, and parsley (optional), and stir with a wooden spoon or sturdy spatula until the dough comes together.

Turn dough out onto a well-floured counter and turn to coat. Knead for 3-4 minutes (don't skimp here!) or until the dough is no longer sticky, and springs back when lightly pressed. Sprinkle more flour onto the counter if the dough is sticky during kneading. The dough should be pretty wet and sticky (kneading kind of makes a mess), so don't be afraid to use plenty of flour as you're rolling out.

Divide the dough into 10 equal pieces (or 12, if you want them a bit smaller; see notes), sprinkle lightly with flour, then cover with a clean kitchen towel or large piece of plastic wrap. Allow to rest for 15 minutes.

Preheat a medium skillet on medium-low heat. While the pan is heating, roll one of the dough portions into an approximately 7-inch circle (you do want it very thin!).

Brush the top surface of the rolled-out dough lightly with extra virgin olive oil.  Don't overdo it, as you don't want greasy flatbreads.  Then gently pick it up and place it in the hot pan (not too hot!), oiled side down.

As it starts to cook, lightly brush the (now) top surface of the dough with a little bit of oil.  Allow to the flatbread to cook on the first side for about 60-90 seconds, until the top is covered with bubbles and the underside is golden around the edges and in spots. 

Then flip to the opposite side and cook for another 60-90 seconds, until a few small golden spots appear, then remove and put on a plate. Don't overcook on the second side.  While it's finishing up, roll out your next round of dough so it's ready (and lightly oil the first side).

Repeat rolling, oiling and cooking with remaining portions of dough.

Sprinkle flatbreads with a bit more chopped parsley when finished, if desired.  Stack flatbreads in a clean kitchen towel after cooking to steam a bit and retain softness.

When they're cool, you can store leftovers in a ziploc bag.  To eat later, you can reheat in a pan without oil for a minute or two on each side OR wrap flatbreads in paper towels and heat in the microwave on low power until warm.