1 envelope active dry yeast (about 2 1/4 teaspoons)
1 tablespoon extra-virgin olive oil, plus more for bowl and brushing
1 1/2 cups all-purpose flour, plus more for working
1 cup semolina flour, plus more for dusting
1 teaspoon salt
1 can (828 millilieters) whole peeled plum tomatoes with juice
2 garlic cloves, minced
2 tablespoons extra-virgin olive oil
2 small shallots, finely chopped (about 2 tablespoons)
1/2 teaspoon coarse salt
1/4 teaspoon freshly ground pepper
Pinch of sugar
340 grams fresh mozzarella cheese, thinly sliced
2 tablespoons freshly grated Parmesan cheese
Freshly ground pepper
Fresh basil leaves for garnish
Pour water into the bowl of an electric mixer. Add sugar and yeast; stir until yeast has dissolved. Let stand until foamy, about five minutes. Add oil, flours, and salt. Fit mixer with paddle attachment; mix until combined. Switch to dough hook; mix five minutes. Transfer dough to a lightly floured surface, and knead a few times with floured hands until smooth and elastic. Transfer dough to a large oiled bowl, and turn to coat; cover with plastic wrap. Let rise in a warm, draft-free place until doubled in bulk, about three hours. (Alternatively, let dough rise in the refrigerator overnight.)
Pulse tomatoes in a blender until smooth; set aside. Put garlic and oil into a medium saucepan. Cook over medium-high heat, stirring, until garlic sizzles, about 40 seconds. Add shallots; cook, stirring, one minute. Add tomatoes, salt, pepper, and sugar. Reduce heat to medium-low. Simmer, stirring occasionally, 30 minutes. Remove from heat; let cool slightly. (Sauce can be refrigerated in an airtight container up to three days.)
Preheat oven to 450 degrees. Preheat a baking sheet. Punch down dough; transfer to a floured work surface. Divide dough in half. Set half aside, and cover with plastic wrap. Roll out remaining dough to 14 by 7 inches, 1/8 to 1/4 inch thick. Sprinkle a pizza peel with semolina flour, and place rolled dough on top.
Brush top of dough lightly with oil. Spread with 1/2 cup sauce, leaving a 1/2-inch border. Top with half the mozzarella. Sprinkle with 1 tablespoon Parmesan, and season with pepper.
Slide pizza onto heated sheet in oven. Bake until dough is golden and cheese is bubbling, 10 to 12 minutes. Meanwhile, repeat process with remaining dough. Let each pizza cool slightly; top with half the basil. Cut into slices, and serve.