Slice the Provola and set it aside. Clean the broccoletti, removing the outermost leaves and the toughest stalks. Rinse under running water and cut away the stalks so that the florets are all more or less the same size.
Heat the oil in a pan over low heat, add the broccoli and cook for about 10 minutes, adding a small amount of water to keep it from sticking to the pan. Adjust the salt and keep warm. In the meantime, cook the pasta in a large pot of salted boiling water for the time indicated on the package.
Drain the pasta, transfer to an ovenproof baking dish that has been buttered or lined with parchment paper, cover with the warm broccoli and the cheese. Finish in a preheated 350° oven for at least 10 minutes until the surface is golden brown. Remove from the oven and serve.