Prepare the dough an hour before you plan on putting the pizza in the oven. The dough needs to double in size which will take more or less that time. For a detailed explanation about this and the dough recipe see Notes below*
To roast the eggplant first cut them in ⅓-½ inch/½ cm thick slices and line them all on a kitchen towel. Sprinkle salt on them to extract the moisture from the slices. It is key to do this. If you skip this step the eggplant slices will become soggy when you roast them.Cover the eggplant with another towel which helps to absorb the moisture. Give them 20-30 minutes to get most of it out. Preheat the oven to 250C/480F or more and lightly grease a baking sheet.
Once the moisture is extracted from the eggplant slices, line the slices on the baking sheet, sprinkle them with dried oregano and roast them for 15-20 minutes in the preheated oven. At the halfway mark, flip the slices to roast them evenly.
Once the dough has doubled in size, divide it into 4 equal pieces and roll them out into pizza bottoms using a bit of flour to prevent the dough from sticking to the rolling pin and the countertop.
To the pizza bottoms add some tomato sauce and spread it out in a thin layer. Make sure to keep the edges free so they can rise in the oven and become crispy with nice air pockets.
Divide the roasted eggplant slices over the pizza bottom and add the mozzarella and parmesan cheese.
Bake the pizza for 5-8 minutes.
Garnish the pizza when they come out of the oven with fresh basil leaves and shaved parmesan (optional)