Stir together sourdough starter, salt, olive oil, and water in a large bowl. Add bread flour and mix until it starts to form a rough ball.
Cover the bowl and let the dough sit for 45-60 minutes.
To stretch and fold the dough: Pull dough from one side and give it a long stretch, then fold dough back to the middle. Turn bowl a quarter turn, stretch again and fold back to the middle. Repeat on all four sides, cover the dough back up, and allow it to rest again.
Over the next few hours, you’ll repeat this process of stretching and folding the dough about every 45 minutes or so. Plan to stretch and fold a total of four times.
On the second round of stretches, fold the cooled roasted garlic cloves and grated parmesan into the dough.
Once you’re done with all the dough stretching, place the covered dough in the refrigerator and let it sit overnight.