For the sauce, heat oil over medium heat in saucepot or Dutch oven. Add onions, oregano, red pepper and season with salt, soften a couple of minutes, add a bit of water, about ¼ cup, and let it absorb. Add garlic, sugar, stir a minute, add tomatoes and passata, wilt in basil if using, and simmer 30 minutes over lowest heat. Remove from heat.

For the dough, if using a mixer, heat water in a small pot or skillet to about 125˚F on an instant-read thermometer, add yeast and sugar and dissolve, add to stand mixer bowl and let stand 5 minutes. Mix flour, salt, 2 tablespoons pecorino cheese and rosemary, if using, in a separate bowl. Start mixer with dough hook on low and add the flour mixture slowly, then stream in EVOO, combine to form sticky dough and let mix 8 minutes on medium. Place dough in oiled bowl and let rise, covered, for 1 hour. 
 
If mixing by hand, heat water in a small pot or skillet to 125˚F on an instant-read thermometer, add yeast and sugar and dissolve, let stand 5 minutes. Mix flour, salt, 2 tablespoons pecorino cheese and rosemary (if using) together in a medium bowl. Put half of the flour mixture into another bowl and mix in the yeast mixture. Drizzle in EVOO and mix in the other half of flour mixture. Mix with your hands to form a shaggy dough, then turn the dough out onto a floured work surface and knead for  10 minutes. Place dough in oiled bowl and let rise, covered, for 1 hour.  

Place a large half-sheet baking pan in oven upside-down or heat a pizza stone at 500˚F with rack at one-above-center.

To prepare the pie, line a second large sheet pan with parchment paper and drizzle with oil. Add the dough and stretch, then turn it over, pull and manipulate it to fill the pan evenly to corners, about 1-inch thick. Once the dough has been stretched to reach the edges, lift the dough up and sprinkle the parchment-lined pan with cornmeal or flour. Pierce the dough all over with the tines of a fork. Place in oven and reduce the heat to 425˚F. Bake dough 15 minutes. Top the dough evenly with all of the sauce and top the sauce with equal amounts of Pecorino and Parm cheese, about ⅓ cup each. Bake another 12 minutes or until sauce sets and edges are brown and crisp. Top with parsley, cut into squares and serve.