Stir the water and yeast together in a large bowl. Add the flour and mix until a shaggy dough forms. Rest for 10 minutes.
Add the salt and knead by hand for 5 to 7 minutes, until the dough is smooth and elastic.
Cover and let the dough rise at room temperature for 2 hours. Divide into 2 balls, cover, and refrigerate for 16 to 48 hours.
Shape and Top:
Remove the dough from the refrigerator 1 to 2 hours before baking. Heat the oven with a pizza stone or steel at its highest setting for at least 45 minutes.
Crush the tomatoes with the olive oil. Drain the mozzarella well and tear it into small pieces.
Dust a work surface with flour. Gently stretch one dough ball into a 12-inch round, leaving the rim slightly thicker. Transfer it to a semolina-dusted peel.
Spread a thin layer of tomato over the dough, leaving the rim bare. Add half the mozzarella and basil. Repeat with the second dough ball.
Bake and Serve:
Slide one pizza onto the hot stone or steel. Bake for 4 to 6 minutes, turning once if needed, until the rim is puffed and blistered and the cheese is melted.
Finish with olive oil and fresh basil. Rest for 1 minute, slice, and serve immediately.
Notes
A long cold fermentation gives the dough better flavor and a lighter rim.
Drain fresh mozzarella well so excess water does not make the center soggy.
If your oven cannot reach pizza-oven temperatures, use a preheated steel under the broiler for the final minute.