Step 1Heat the olive oil in a 4-quart soup pot over medium heat and cook the onions until they soften, about 3 minutes. Add the garlic and cook until it becomes fragrant, about 2 minutes. Add the coarsely chopped greens to the pot, a handful at a time, and let them wilt, stirring constantly.
Step 2Add the diluted stock and the salt and slowly bring to a simmer, then cook until the greens are soft (but not darkened or faded), about 10 minutes.
Step 3While the greens are cooking, cook the pasta in a large pot of rapidly boiling salted water until tender, about 5 minutes. Drain and set aside until the soup is done.
Step 4Coarsely shred the greens with an immersion blender. Some will become pureed, but mostly they should be shredded. If you don't have an immersion blender, a food processor will do a better job than a stand blender. Transfer half the greens and liquid to a food processor and carefully puree until the greens are finely chopped. Reserve in a mixing bowl and repeat with the remaining greens and liquid. Wipe out the soup pot and return the greens and liquid to it.
Step 5Bring the soup to a simmer, and stir in the cooked pasta and 1 teaspoon vinegar. If the pasta clumps together (it probably will), let it warm and stir it again to break it up. Season with the pepper and the fennel seed. Taste, and add more salt or vinegar if needed.
Step 6To serve, ladle the soup into heated shallow bowls and garnish with a generous grating of Parmigiano-Reggiano.