Put the barley in a large saucepan with enough water to cover by 3 inches and a large pinch of salt. Bring to a slow, steady simmer, then cover, and cook until the barley is fully tender, 30 to 45 minutes. Drain, saving the water in a bowl for the soup.

While the barley is cooking, detach the florets and any small leaves from the broccoli. Peel the main stems and the florets’ stems. Rinse the broccoli well.

Fill a large soup pot with water and bring to a boil. Add 2 tablespoons salt and the thick, main broccoli stems. (The salt is to keep the broccoli green and it will not make it too salty.) Cook for 7 or 8 minutes, then add the florets. When the water returns to a boil, cook for another 10 minutes or so, then drain. Chop the broccoli rather fine and set aside.

Put the olive oil and garlic in the soup pot, turn on the heat to medium, and cook, stirring frequently, just until the garlic turns a deep ivory, about 1 ½ minutes.

Add the broccoli and cook for 2 or 3 minutes, turning it over from time to time to coat it well. Add the cannellini beans and cooked barley and stir once or twice.

Add enough of the barley cooking water to cover by at least 2 inches, using fresh water if you need more. Put in the bouillon cube and several grindings of pepper, and stir for 15 or 20 seconds. Bring to a simmer and cook for about 5 minutes. Taste and correct for seasoning. Serve with a trickle of olive oil in each bowl.