Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Divide the dough into 3 pieces. Stretch the dough thinly, pressing the edges into the counter so it doesn't spring back. Let it rest a few minutes, then transfer each piece to the prepared baking sheet.
Using a mandoline or slicer, slice the potatoes and shallot 1/16-inch thick. Spread a bit of the sliced shallot over each crust, then top with a single overlapping layer of potatoes.
Sprinkle with the rosemary, 1/2 teaspoon salt and pepper. Drizzle with the olive oil and bake until the crust is crisp and deep brown, about 20 minutes. Serve warm or at room temperature.