To make the crust: Mix the dough ingredients, and knead to make a smooth crust. This will take about 7 minutes at medium-low speed in a stand mixer. You can also make the dough in a bread machine set on the dough or manual cycle.
Place the dough in a lightly oiled bowl, cover, and let rise till very puffy, about 60 minutes.
While the dough is rising, ready your 14" deep-dish pizza pan. Grease it with non-stick vegetable oil spray, then pour in 3 to 4 tablespoons olive oil, tilting it to cover the bottom of the pan, and partway up the sides.
Stretch the dough to make as large a circle as you can. You can do this on a lightly oiled baking mat, if you choose; or simply stretch the dough in your hands.
Lay the dough in the pan, and stretch it towards the edges till it starts to shrink back. Cover, and let it rest for 15 minutes. Start preheating the oven to 425°F while the dough rests.
Stretch the dough to cover the bottom of the pan, then gently push it up the sides of the pan. The olive oil may ooze over the edge of the crust; that's OK. Let the crust rest for 15 minutes or so, as your oven comes up to 425°F
Bake the crust for 10 minutes, until it's set and barely beginning to brown. While it's baking, prepare the filling.
Drain the tomatoes thoroughly. Combine them with herbs, and the garlic and sugar (if you're using them). Add salt to taste.
Cover the bottom of the crust with the sliced mozzarella, fanning it into the crust. Add the sausage (or sautéed vegetables), then the tomato mixture.
Sprinkle with the grated Parmesan, and drizzle with the olive oil.
Bake the pizza for about 25 minutes, or until the filling is bubbly and the topping is golden brown. Remove it from the oven, and carefully lift it out of the pan onto a rack. Allow the pizza to cool for about 15 minutes (or longer, for less oozing) before cutting and serving.