Knead 1 Tbsp. olive oil into dough, cover with a towel, and let rest 10 minutes. Roll out dough on a lightly floured surface to a 16-by-11-inch rectangle. Transfer to a large, shallow baking sheet.
Cook onion and garlic in 1 Tbsp. oil in a medium skillet over medium heat, stirring, until soft, for about 7 minutes. Let cool, then scatter over dough.
Preheat oven to 425°. Peel and thinly slice potatoes. Arrange in an even layer on dough. Drizzle cream and 2 Tbsp. oil over top. Then sprinkle on 2 Tbsp. Parmesan, salt, crushed red pepper and black pepper.
Bake for 25 minutes, sprinkle rosemary on top and bake for 10 minutes more. Top with remaining 1 Tbsp. and 1 tsp. oil and 2 Tbsp. Parmesan. Serve hot.