Make the dough: Fill a small bowl with hot tap water. Let the bowl sit 2 minutes, then dump the water. In the warmed bowl, combine the yeast, 1 tablespoon flour, the sugar and 1/4 cup warm water (105 degrees F to 115 degrees F). Let stand about 5 minutes. (The mixture will be creamy and slightly bubbly; if it isn't, start over with fresh new yeast.)
In a large bowl, mix 2 1/2 cups flour and 2 teaspoons salt. Make a well in the center and stir in the yeast mixture, olive oil and 3/4 cup warm water (105 degrees F to 115 degrees F) with a wooden spoon. Mix until the dough starts to come away from the side of the bowl (it will be sticky). Turn out onto a lightly floured surface; knead with floured hands until soft and elastic, about 8 minutes. Form into a ball.
Brush another large bowl with olive oil. Add the dough and roll to coat with the oil. Tightly cover with plastic wrap and let rise in a warm place until doubled in size, 1 to 1 1/2 hours. Meanwhile, put a pizza stone on the lowest oven rack and preheat to 500 degrees F. Let the stone preheat, about 1 hour.
Make the sauce: Combine the olive oil, oregano, minced basil, tomatoes and 1/4 teaspoon salt in a small saucepan over medium heat; bring to a simmer, stirring frequently. Reduce the heat to low and cook until slightly thickened, about 10 minutes. Transfer to a food processor and puree until smooth. Return the sauce to the pan and cook over medium heat until reduced to 1 cup, about 10 minutes. Season with pepper to taste.
Transfer the dough to a floured surface and cut in half. Form each half into a disk and roll out into a 10-inch circle with a lightly floured rolling pin. (I like my pizza paper-thin!) Pinch around the edge to form a crust.
Sprinkle a pizza peel with cornmeal and carefully slide one round of dough onto the peel. Jerk the peel in a back-and-forth motion once or twice to make sure the dough does not stick. (If the dough is sticking, add extra cornmeal.) Drizzle the dough with olive oil, sprinkle with salt and top with half of the sauce, leaving a small border.
Transfer the dough to the hot stone in the oven, using a jerking motion to slide the dough off the peel. Bake 5 minutes. Using the peel, rotate the pizza for even browning and top with half of the mozzarella. Bake until the cheese melts and the crust is golden brown and crisp, 3 to 5 more minutes. Remove from the oven using the peel, transfer to a cutting board and scatter half of the basil on top. Repeat to make the second pizza.