Step 1 Cook the garlic in the olive oil in a 4-quart soup pot over medium heat until the garlic has softened, about 3 minutes. Add the coarsely chopped greens to the pot. They will come close to the top of the pan, but quickly wilt down when cooked. Cook, stirring, until wilted, about 4 minutes.
Step 2 Add the diluted stock and the salt and slowly bring to a simmer, then cook 5 minutes (less, if the colors begin to darken and fade).
Step 3While the greens are cooking, heat the rice and water in a 1-quart saucepan over medium-high heat. When the water comes to a boil, reduce the heat to low and cover tightly. Cook until there is no water left in the bottom of the pan and the rice is tender, about 10 to 15 minutes. Remove from the heat and cool, covered, until ready to use.
Step 4Transfer half the greens and liquid to a food processor and carefully puree until the greens are finely minced. Reserve in a mixing bowl and repeat with the remaining greens and liquid.
Step 5Wipe out the soup pot and return the greens and liquid to it. Bring the soup to a simmer, and stir in the rice and the vinegar. Season with a generous grinding of pepper. Taste, and if the soup needs more salt or vinegar, add it.
Step 6To serve, ladle the soup into heated shallow bowls and garnish with a generous grating of Parmigiano-Reggiano.