Make the dough: Combine the warm water and yeast in a small bowl, stirring to dissolve the yeast. Combine the flour and salt in a medium bowl. Add the yeast mixture to the flour and stir to make a shaggy dough. (The dough should be tacky. If it feels too wet and sticky, add flour, 1 tablespoon at a time; if it's too stiff, add a little water.) Transfer to a lightly oiled surface and knead until smooth and elastic, about 3 minutes. Place an inverted bowl over the dough and let rise slightly, 30 minutes. Divide the dough into 4 pieces and form each into a ball; arrange 3 inches apart on a lightly oiled baking sheet. Rub the tops of the dough lightly with olive oil and cover the baking sheet with plastic wrap. Refrigerate overnight.
Remove the dough from the refrigerator about 2 hours before baking; let sit, covered, until ready to use. One hour before baking, put a pizza stone or inverted baking sheet on the middle oven rack and preheat to 500 degrees F (or 550 degrees F if your oven goes that high).
Make the sauce: Combine the tomatoes and their juices with 1 teaspoon salt in a blender; blend until smooth.
Generously sprinkle a pizza peel or an inverted baking sheet with cornmeal. Place 1 ball of dough upside down on the cornmeal using floured hands. Gently pull the dough into an 8- to 10-inch circle, reflouring your hands as needed and being careful not to deflate the dough. Spread about 1/4 cup tomato sauce on the crust; top with one-quarter of the mozzarella. Drizzle with 1 to 2 teaspoons olive oil and season with salt.
Slide the pizza onto the hot stone and bake until the crust is dark golden brown and the cheese is bubbling, 7 to 9 minutes. Transfer to a cutting board and sprinkle with basil. Let cool 2 minutes before slicing. Repeat to make 3 more pizzas.
Refrigerating the dough overnight gives this crust a slightly chewy texture.