Add the tomato paste, stir, and cook until caramelized, about one minute. It will give a pinkish and inviting colour to your pasta and potatoes.

Add the diced potatoes, stir, and cook on low heat for about five minutes, taking care not to brown the potatoes.

Pour in 1⅔ cups/400 ml hot water (it should be enough to cover the potatoes), add the Parmigiano-Reggiano rind, and cook on a medium flame for about 20 minutes, stirring occasionally, until you can easily mash the potatoes with a wooden spoon against the edges of the pot.

Pour in the remaining hot water, and the pasta, and stir thoroughly. Simmer until the pasta is al dente, about 10 minutes.

When the pasta is cooked through, and the soup is thick, remove the pot from the heat, add the grated Parmigiano Reggiano, and stir energetically. Taste and adjust the seasoning with salt.

Ladle the soup into warmed bowls, drizzle each serving with some olive oil, sprinkle with freshly ground black pepper, and serve. The Parmigiano-Reggiano rind can be cut into smaller pieces and added to the bowls.

Any leftover soup can be refrigerated for up to two days. Reheat gently over low heat, adding a bit of water as necessary to thin.