Mix the dough: In a large bowl, whisk together the flour, salt, and instant yeast. Add the sourdough discard, water, and oil. Stir with a spatula until a shaggy dough forms. Knead the dough on a lightly floured surface until it is smooth, about 2 minutes.
Let the dough rise. Place the dough in a clean bowl and drizzle with a little olive oil, turn the dough to coat. Cover the bowl with plastic wrap, and leave it in a warm place to rise until the dough has doubled in size, about 1 hour.
Preheat the oven. Place a cast-iron skillet or pizza stone in the oven and preheat the oven to 550ºF. Cut a sheet of parchment paper into 6 6-inches squares.
Portion the dough. Turn the dough out onto a lightly floured surface and gently punch it down. Divide the dough into 6 equal pieces. Cover the balls of dough with a kitchen towel and let them rest for 30 minutes.
Roll out each ball. Flatten the first ball and using a rolling pin roll it out into a 6-inch circle. When rolling the dough out you want to do so gently to avoid forcing all of the air out. Once you have rolled the dough out transfer it to one of the sheets of parchment paper. Roll the remaining balls out and let them all rest for 15 minutes.
Bake the pitas. Transfer the rounds (parchment paper and all) to your cast-iron skillet or pizza stone. The size of your vessel will determine how many you can cook at one time. Bake for 2-3 minutes until golden brown. Transfer the pitas to a bowl and cover with a kitchen towel. The steam softens the pitas and gives them the perfect texture. Repeat the baking process with the remaining pitas.