To get a perfect, cracker-like crust, preheat your pizza stone on the oven rack for at least 30 minutes before baking your pizza. Slideshow: More Pizza Recipes
In a small bowl, whisk the water with the yeast and sugar. Let stand until foamy, 10 minutes. In a large bowl, whisk the 3 cups of flour with the salt. Stir in the yeast and 1 tablespoon of oil until a dough forms. Turn the dough out onto a lightly floured work surface and knead until smooth. Lightly oil a large bowl and transfer the dough to it. Cover and let stand in a warm place until doubled in bulk, about 1 hour.
Preheat the oven to 450° with a pizza stone set on the middle rack. Roll the dough into 4 balls and arrange them on a parchment-lined baking sheet spaced a few inches apart. Cover the dough loosely with plastic wrap and let stand in a warm place for 30 minutes.
In a food processor, pulse the tomatoes with the oil until a chunky puree forms. Season with salt and pepper.
Dust an inverted baking sheet with cornmeal. On a lightly floured work surface, using a lightly floured rolling pin, roll out 1 piece of dough to a 10-inch round. Transfer to the inverted baking sheet. Spread 1/4 cup of the tomato sauce all over the dough, leaving a 1-inch border, then top with one-fourth of the cheese. Carefully slide the pizza onto the hot stone and bake until the crust is golden and crisp and the cheese is melted, about 10 minutes. Transfer the pizza to a work surface, top with one-fourth of the prosciutto and garnish with arugula. Slice and serve immediately. Repeat to make 3 more pizzas.
The tomato sauce can be refrigerated for up to 2 days.
Doppio zero, or 00, is a fine Italian flour that's available at specialty food shops and from amazon.com.