Preheat an oven to 400°F. Line a large rimmed baking sheet with parchment paper.
On a floured work surface, roll out the puff pastry into a rectangle . Transfer the dough to the baking sheet.
Arrange fig slices and half of cheese on top.
Bake until the crust puffs, about 15 minutes.
Toss arugula with a splash of olive oil and salt and pepper, to taste. Top tart with arugula and prosciutto pieces. Cut into small portions and serve.