In the bowl of a stand mixer fitted with a dough hook, add 1/4 cup of the water and sprinkle the yeast on top. Let sit for 5 minutes then whisk it together.
In a separate bowl add 3 tbsp of the oil to the remaining water (1 cup)
Once the yeast has been stirred add the remaining water/oil mixture to the stand mixer
Add the flour, salt, 1/2 cup of the Parmesan and the pesto and mix on low speed until the dough comes together, about 5-7 minutes.
Transfer the dough to a floured work surface and knead by hand into a ball shape.
Place the dough back into the bowl that had the oil/water mixture and cover with a clean towel.
Place in a warm area and let the dough rise for 1 hour or doubled in size.
After 1 hour dump the dough out onto a floured work surface and punch all the air out of it.
Knead back into a ball and repeat for the second rise process, cover for another hour.
Spray a 9x13 inch baking pan with non stick spray and preheat the oven to 450 degrees F.
After the dough has completed its second rise, dump it out into the prepared baking pan and using your fingers flatten it out evenly to fill the pan making sure to push it into the corners.
Cover and let rise for another 30 minutes.
After 30 minutes pour the remaining 1/2 cup of olive oil over the dough making sure to cover all of it.
Using your fingertips press down on the dough to create the holes. The easiest way is to start at one end of the pan and move towards the other end.
Sprinkle with the remaining Parmesan over the top.
Sprinkle generously with some flaked sea salt.
Place in the oven and bake for 30 minutes.
Let cool slightly before cutting into squares and serve with extra olive oil or dipping.