Arrange oven racks in the lower and upper third of the oven. Heat the oven to 475° F.
Heat 4 tablespoons of the oil in a large, nonstick skillet over medium heat. Add the onions and cook until translucent and soft.
Roll out the dough on a well-floured surface to make two 8- x 16-inch rectangles or two 12-inch rounds and transfer to two ungreased baking sheets (or two 12-inch pizza pans). Layer the dough with the sweet potato slices, overlapping them slightly and forming three rows (or in a circular pattern if making round pizzas). Top the potato slices with the onions and rosemary. Drizzle the pizza with the remaining olive oil and season well with salt and freshly ground pepper.
Bake pizzas 15 to 18 minutes, or until the edges of the pies are crisp and lightly browned and the sweet potatoes are soft. Top with Parmesan and return to oven 1 to 2 minutes, until cheese melts.
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