If the dough springs back in step 2, let it rest for a few minutes before trying to roll it again.
Adjust oven rack to middle position and heat oven to 500 degrees. Brush rimmed baking sheet with oil. Combine mascarpone, warm water, rosemary, ¼ teaspoon salt, and ¼ teaspoon pepper in bowl.
Divide dough into 4 equal pieces. Roll each piece into 5 by 7-inch rectangle and transfer to prepared sheet. Spread 2 tablespoons mascarpone mixture on each rectangle, leaving ½-inch border. Sprinkle evenly with bacon, dates, remaining ¼ teaspoon salt, and remaining ¼ teaspoon pepper, then top with fontina, apple, and onion.
Bake until cheese is melted and crust is golden, 12 to 14 minutes, rotating sheet halfway through baking. Let flatbreads cool on sheet for 5 minutes. Slice and serve.
