Stretch and roll out two 1-pound balls of pizza dough (thawed if frozen) to 14-inch ovals. Place on two baking sheets and freeze until firm, about 1 1/2 hours. Wrap crusts in plastic and freeze for later use.
Preheat oven to 350 degrees. Halve 14 plum tomatoes. On two large rimmed baking sheets, arrange tomatoes, cut side up, and sprinkle with 1/4 teaspoon sugar. Bake until softened and edges are crinkled, about 1 hour. Let cool. Cover and refrigerate for later use.
Preheat oven to 475 degrees, with racks in upper and lower thirds. Lightly oil two large baking sheets. Place crusts on sheets and brush each with 1 tablespoon oil.
Top one crust with tomatoes, dollop with ricotta, then sprinkle with Parmesan; season with salt and pepper. Top second crust with an even layer of potatoes, sprinkle with rosemary, then drizzle with 1 tablespoon oil; season with salt and pepper.
Bake pizzas until crusts are browned, about 11 minutes, rotating sheets halfway through. Sprinkle ricotta-tomato pizza with basil.
This recipe makes a double batch of pizza, so you can feed a crowd tonight -- or enjoy leftovers for lunch tomorrow.