In a mixing bowl, combine warm water and yeast. Let sit until foamy, about 5 minutes, indicating activation.
Add olive oil, salt, and flour to the yeast mixture. Mix with a spoon or dough hook until a shaggy dough forms, then knead on a floured surface for about 5 minutes until smooth and elastic.
Shape the dough into a ball, place it in a lightly oiled bowl, and cover with a damp cloth. Let rise in a warm place for about 30 minutes, or until doubled in size.
Preheat the oven to 475°F (245°C). If using a pizza stone, place it in the oven during preheating.
Meanwhile, resume the dough and punch it down to release excess air. Roll or stretch it into a circle about 12 inches in diameter on a floured surface.
Transfer the shaped dough onto a parchment-lined baking sheet or preheated pizza stone. Brush the surface lightly with olive oil.
Spread crushed tomatoes evenly over the dough, leaving a 1-inch border for the crust. Sprinkle shredded mozzarella generously over the sauce.
Place the pizza in the oven and bake for 12-15 minutes, or until the crust is golden brown and cheese is bubbling and slightly browned.
Remove the pizza from the oven, sprinkle with chopped fresh basil if desired, and let sit for 2 minutes to settle.
Slice and serve hot, with the crust looking crispy and cheese melted to perfection.
