Add the sourdough starter, milk, yogurt, and olive oil to the bowl of a stand mixer and combine the ingredients using the paddle attachment.
Add the flour and salt to the mixture in the bowl, using the hook attachment to combine on low speed until a stiff, slightly shaggy dough forms (5-6 minutes).
Form one large ball from the dough. Return the dough to the bowl, cover it with plastic wrap or a clean dish towel, and let the dough rise until it doubles in size (about 8 hours).
Divide the risen dough into 8 equal portions, form each one into a ball, and place them onto a baking sheet lined with parchment paper. Then, loosely cover the portioned dough with plastic wrap or a clean dish towel.
Let the dough rest for about 1 hour or refrigerate overnight, if needed.
Use a rolling pin to flatten each of the 8 dough balls until they form ⅛-inch thick rounds. Heat a medium-sized skillet over low-medium heat. Place a teaspoon of olive oil or ghee into the skillet.
Add a piece of dough to the skillet and cook until it bubbles on the top and turns brown and charred on the bottom (3-5 minutes). Flip the flatbread to cook the other side until charred spots appear (another 2-3 minutes). Transfer your naan to a waiting wire rack while you repeat this step with each of the remaining pieces of dough.
Enjoy your discard naan bread warm or at room temperature!
