1.
Activate the yeast. Combine the warm water, sugar, and yeast. Stir until the yeast is hydrated and let it stand until you begin seeing bubbles or foam. The water should feel neither hot nor cold to the touch.
2.
Combine the dry ingredients. Place the flour in a large mixing bowl and mix in the salt. Keep the salt separate from the yeast while the yeast is initially activating because salt can slow its activity.
3.
Make the dough. Add the olive oil and activated yeast mixture to the flour. Stir until most of the flour has absorbed the liquid and a rough dough forms.
4.
Knead thoroughly. Transfer the dough to a clean work surface. Knead for about 10 minutes, folding the dough over itself and pushing it forward without tearing it. Continue until smooth, elastic, and springy. When pressed with a finger, properly kneaded dough should quickly spring back.
5.
Shape and begin the first rise. Pull the outer edges underneath the dough to create a smooth ball. Lightly oil a large bowl and place the dough inside. Coat the surface lightly with oil so it does not stick while rising. Cover tightly.
6.
Let the dough rise. Let rise for about 1 hour at room temperature. For considerably more flavor, refrigerate and ferment the dough for up to 24 hours instead. The longer fermentation produces a more developed, complex pizza-dough flavor.
7.
Re-knead the dough. Turn the risen dough onto your work surface and knead for another 1–2 minutes. This redistributes the air bubbles produced during fermentation.
8.
Divide the dough. Divide into 4 approximately equal pieces and shape each into a smooth ball. The full batch is intended to make about four good-sized pizzas.
9.
Second rise. Lightly flour the dough balls, cover with a clean towel, and allow them to rest and rise for another 1 hour.
10.
Preheat the oven. Heat your oven as hot as it will safely go. Place a pizza stone, cast-iron surface, or upside-down baking sheet inside while the oven preheats. Preheating the baking surface creates the strong bottom heat needed for a crisp pizza crust.
11.
Make the tomato sauce. Place the whole canned tomatoes in a bowl and crush them by hand or blend briefly with an immersion blender. Season with salt. A simple uncooked tomato sauce works well because it cooks directly on the pizza.
12.
Prepare the cheese. Tear fresh mozzarella into relatively small pieces so it can be distributed evenly across the pizza.
13.
Shape the pizza. Place one dough ball on a lightly floured surface. Press gently outward with your fingertips while leaving some air in the outer edge. Continue stretching with your fingers and hands until you have a thin round pizza with a slightly thicker rim. Avoid crushing all the bubbles in the dough; those bubbles help produce the airy, blistered crust.
14.
Prepare your pizza peel. Dust a pizza peel or upside-down baking sheet with semolina flour. Transfer the stretched dough onto it. Give it a small shake to make sure the dough can slide freely.
15.
Add the toppings quickly. Spread a thin layer of tomato sauce over the dough, leaving the edge uncovered. Scatter torn mozzarella evenly over the surface. Avoid overloading the pizza, which can make it difficult to transfer and can prevent the crust from becoming crisp.
16.
Bake immediately. Slide the pizza onto the fully preheated baking surface. Bake until the bottom is crisp, the crust is deeply golden brown, and the mozzarella has melted and developed browned spots.
17.
Finish the pizza. Remove from the oven and scatter fresh basil over the top. Finish with a small drizzle of extra-virgin olive oil if desired.
18.
Slice and serve. Allow the pizza to sit briefly before slicing. Repeat with the remaining three dough balls.