Peel the potatoes and cut them into small dices of about 1 cm (½ inch).
Add the olive oil and butter in a large pan and turn on the heat. Add the potatoes and the soffritto (or onion) and sautèe for about 5 minutes.
Add the tomato paste, salt, black pepper and rosemary, then add the pasta to the pan and add all the water at once.
Bring to a boil than turn down the heat and simmer for about 20 minutes uncovered, so both the pasta and potatoes are fully cooked. If the water did not reduce to a creamy sauce, turn up the heat and cook another 5 minutes. If instead it reduced too much, add a few more tablespoons of water.
After the cooking time, add the diced Scamorza cheese to the pan and mix well until it's fully melted into the sauce.
Season again with salt and black pepper if needed and serve immediately.
Notes
You can find the recipe for Soffritto (Mirepoix) at this link. It's a mix of minced onion, carrot and celery very much used in Italian cooking to give more flavor to the dish. If you don't have it available in your freezer, you can substitute it with just an onion.