Place the starter in a large bowl or the bowl of a stand mixer.
Add the flours, salt, yogurt, and oil. Mix well and begin adding water. Once it all incorporates, let rest for 20 minutes.
Knead for 10 minutes to get a very soft and pliable dough. If it feels too tight, add a few drops of water. Too sticky? Add a bit of flour.
Form into a ball and place in an oiled bowl. Turn to coat all sides. Cover and set aside to rest for at least four hours or overnight in the refrigerator.
Uncover and punch down. Divide into 8-10 pieces. Form each piece into a ball and let rest for 10 minutes.
On an oiled work surface, take each ball and use the heel of your hand to work into a teardrop shape. Continue until all are shaped.