Rinse broccoli well. Chop the florets into bite sized pieces. Peel off the tough outer layer of the stalks and chop into small cubes. Set aside.
For the soup
In a large sauce pan, heat olive oil on medium heat and sweat the diced onion for 3 minutes.
Stir in the cubed potato pieces, add a pinch of salt and cook, covered, on low heat for 10 minutes.
Uncover, add the diced tomatoes and cook, stirring occasionally, for 5 minutes on medium heat.
Add the broccoli, 1/2 tsp of salt and cook, stirring, for 2 minutes until the broccoli pieces are completely coated in the tomato sauce.
Pour in 6 cups of water, bring to a boil and add the cheese rind. Lower the temperature to a simmer and cook, covered, for 20 minutes until the broccoli and potato pieces are tender.
Add pasta of your choice and cook until al dente, about 8-10 minutes. Add more salt, if needed.
Drizzle lightly with olive oil when done. Serve hot with plenty of grated Parmigiano and/or Pecorino cheeses at the table.
Notes
Add any small pasta of your choice including shells, or even spaghetti broken into small pieces.
Vary the amount of diced tomatoes according to how 'tomatoey' you prefer your soup.
For a non-vegetarian version of this soup, add some diced pancetta or sausage without the casing in step 1 of the recipe.
Let the soup sit for about 30 minutes before serving. The broth thickens to create a wonderful texture that I prefer!