With the machine running, pour the oil and then the water through the feed tube and process until the dough forms a ball, about 30 seconds. If after 30 seconds the dough is sticky and clings to the blade, add the remaining 1/4 cup flour 1 tablespoon at a time. Turn the dough out onto a work surface.

Divide the dough in half and place each piece in a gallon-sized, heavy-duty zipper-lock bag and seal. Refrigerate overnight or up to 48 hours.

Process the tomatoes in a food processor until smooth, about 5 pulses.

Heat the oil and garlic in a medium saucepan over medium heat until the garlic is fragrant, about 30 seconds. Stir in the tomatoes; bring to a simmer and cook, uncovered, until the sauce thickens, about 15 minutes. Season with salt and pepper to taste.

One hour before baking the pizza, adjust an oven rack to the lowest position, set a pizza stone on the rack, and heat the oven to 500 degrees.

Remove the dough from the plastic bags. Set each piece in the center of a lightly floured large sheet of parchment paper. Cover each with two 18-inch lengths of plastic wrap, overlapping them in the center; let the dough rest for 10 minutes.

Setting one piece of dough aside, roll the other into a 14-inch round with an even thickness, using the tackiness of the dough against the parchment to help roll it. If the parchment wrinkles, flip the dough sandwich over and smooth the wrinkles with a metal bench scraper.

Peel the plastic wrap off the top of the rolled dough. Spread 1/2 cup of the tomato sauce to the edges of the dough. Sprinkle with 1 cup of the cheese.

Slip the dough with the parchment onto a pizza peel or rimless baking sheet. Slide the pizza, parchment and all, on to the hot pizza stone. Bake until a deep golden brown, about 10 minutes. Remove the pizza from the oven with a pizza peel or pull the parchment with the pizza onto a baking sheet. Transfer the pizza to a cutting board, slide the parchment out from under the pizza, and slide it onto a wire rack. Cook 2 minutes until crisp; slide to a cutting board, cut into wedges, and serve.

While the first pizza is baking, repeat steps 6 and 7 to roll and top the second pizza; allow the baking stone ot reheat for 15 minutes after baking the first pizza, then repeat step 8 to bake the second pizza.