Invert a large baking sheet and place it on a rack in the lower third of the oven; preheat the oven to 500°. Invert a second baking sheet on a work surface and cover it with a sheet of parchment paper. Stretch the pizza dough to fit the parchment paper.
Slide the pizza and the parchment from the cool baking sheet to the hot baking sheet in the oven. Bake until golden, about 5 minutes. Cut into pieces and sandwich chocolate-hazelnut spread and ice cream between 2 pieces.