To prepare the cannellini broth, combine the brodo and battuto in a soup pot and simmer over medium heat, covered, for about 30 minutes. Strain, returning the liquid to the soup pot.

Bring the bean broth to a lively simmer, then add the farro. Lower the heat and simmer, covered, until the grains are very tender, about 40 minutes.

Remove from the heat. Strain the faro, and add its liquid back to the soup pot.

Reserve about one quarter of the farro and pass the remainder through a vegetable mill or puree in a food processor until smooth. Add the pureed farro back to the broth and stir to combine well.

Bring the soup to a gentle simmer. It should have the density of heavy cream; if it's needed, add a little hot water. Add the salt to taste and the reserved farro. Add the shrimp and gently simmer until cooked, 5 to 10 minutes.

In the meantime, fry the crostini in butter, preferably in a nonstick pan. Stir the marjoram into the soup and serve with the crostini.