Combine the flour, salt, sugar, yeast and olive oil in a large bowl (or the bowl of your stand mixer). Using an electric mixer with a dough hook attachment, a stand mixer with dough hook attachment, or by hand, gradually add the water until the dough comes together. Start with 1½ cups and add more as needed. Knead the dough for 5 minutes on low speed until the dough forms a soft ball. Alternatively, mix with a wooden spoon and knead the dough by hand for 10 minutes.

Remove the dough from the bowl and grease the bowl with a little olive oil. Return the dough to bowl, cover with a damp kitchen towel or plastic wrap and let it rise for 60 to 90 minutes, until it doubles in size. (Or if making ahead, refrigerate overnight.)

To make the sauce, heat the olive oil in a medium sauté pan over medium-low heat. Add the garlic, dried oregano, and pinch of red pepper flakes. Cook for 30 seconds, then add the tomato purèe, tomato paste, olive oil, balsamic vinegar, sugar, and salt. Simmer sauce over low heat for 20 minutes, stirring occasionally. Remove from heat and allow to cool.

Generously grease a large sheet pan with olive oil. Stretch the dough and press it into the baking pan. Cover with plastic wrap and let it rise for 30 to 60 minutes.

Pre-heat the oven to 450°F.

Reserve about ¾ cup of the sauce and set it aside. Spread the remaining sauce evenly over the dough. Bake in a pre-heated oven for 15 minutes. Then spread the reserved sauce over the pizza and sprinkle a couple tablespoons of the grated cheese on top. Continue to bake for another 5 to 7 minutes, until the crust is nicely browned on the bottom. Transfer the baking sheet to a cooling rack and let the tomato pie cool on the sheet for a few minutes before transferring to a cooling rack. Cool for at least 15 minutes.

Sprinkle the rest of the Parmesan cheese on top of the sauce. If using fresh basil, tear up the leaves and sprinkle it over the pizza. Serve the tomato pie warm or at room temperature.