Coat rimmed baking sheet with 2 tablespoons oil. Combine water and remaining 1 tablespoon oil in a 1 cup liquid measuring cup. Using a stand mixer fitted with a paddle attachment, mix flour, yeast, sugar, and salt on low speed until combined. With mixer running, slowly add water mixture and mix until dough comes together, about 1 minute. Switch to dough hook attachment. Increase speed to medium-low and mix until dough is smooth and comes away from sides of bowl, about 10 minutes.
Transfer dough to greased baking sheet and turn to coat. Stretch dough to 10 x 6 inch rectangle. Cover with plastic wrap and let rise in warm place until doubled in size, 1 to 1 1/2 hours. Stretch dough to corners of pan, cover loosely with plastic, and let rise in warm place until slightly puffed, about 45 minutes. Meanwhile, adjust oven rack to lowest position and heat oven to 500 degrees.
For the Topping:
Place tomatoes in colander and drain well. Place drained tomatoes in a small bowl. Using a potato masher, mash the tomatoes until just crushed. Add oil, garlic, oregano, basil, and salt to the bowl of tomatoes. Sprinkle cheeses over dough, leaving 1/2 inch border around edges. Top with tomato mixture and bake until well browned and bubbling, about 15 minutes. Slide pizza onto wire rack and let cool for 5 minutes before cutting into squares and serving.
Dough should be prepared at least 2 hours before preparing pizza.