Parathas are a flaky Indian bread. Often they're stuffed with potatoes or onions or other things (you may have encountered them in this form in Indian restaurants). These are unstuffed, and also not quite really parathas because they're made with olive oil rather than ghee. The proportions and technique are partially from Indian Home Cooking and partially from my observations of my friend A.'s mother Tara.
The flour we use for almost everything is half King Arthur all-purpose flour (which has more protein than most all-purpose flours) and half King Arthur "white wheat" flour, a mild-tasting whole wheat. The large flour jar on our counter is just always filled with a 50/50 blend of these, so I scoop out 1 1/2 cups of that. In this case, the mixture is quite authentic. If you have to pick one or the other -- white vs. whole wheat -- I'd choose whole wheat. You're going for both flakiness and heartiness, and the gluten in pure white flour makes that tricky to achieve.
The dough is 1 1/2 cups flour, half whole wheat and half white, plus a teaspoon of salt. Add warm water little by little with one hand as you mix it in with the other, until it comes together as a slightly damp dough. That will probably be about 3/4 cup of water, though it depends on the weather and how old your flour is and other things.
Knead it and let it rest, covered with a damp towel for at least half an hour.
Divide into nine equal pieces. Roll each piece into a ball, and set them under the damp towel to rest again for at least 15 minutes.
Set out a bowl of flour for dusting, a small bowl of olive oil with a soup spoon, and a small knife.
For each piece, use your thumbs to flatten it into a disk, then roll out to about a 5" round.
Use the back of the spoon to coat the disk lightly with oil, then dust with flour.
Make a cut with the knife from the center out to the edge, then roll it up into a cone.
Pinch the top and then flatten into a ball.
Do this for each piece, putting them back under the cloth as you go. Once you've rolled out and rolled up each one, then start at the beginning and roll each one out into a 5" round. Stack them on a small plate and cover with a dry towel or, better yet, put the whole thing into a plastic bag or under plastic wrap.
Clean up and set out a bowl or plate where you can put the parathas (or parathoids, since they're inauthentic) when they're cooked, so you can keep them covered with a clean dry cloth. Have butter nearby.
Heat a griddle over medium-high heat. Put your bowl of oil + spoon nearby. The cooking process goes like this:
Put a piece of dough on the griddle and let it cook until little bubbles appear, about 30 seconds to a minute. Then flip it.
Use the back of your spoon to coat the disk very lightly with oil, making circular movements all the time as you go.
Flip the dough again.
Do the same for the other side and then keep on moving the spoon, spiraling in and out, as the dough puffs up.
Cook about 1 minute to 90 seconds. Flip the bread and cook the other side the same way, moving the spoon over the surface all the time.
When both sides are cooked (crisp on the outside, no damp looking bits, and well spotted with golden brown), transfer to your covered container. Put a little dab of butter on top. Repeat and stack up all nine parathas in the same way.