Place the farro in a medium pot with cold water to cover by an inch. Soak for 20 minutes.
After 20 minutes, drain the soaking water and add fresh water to cover the farro by two inches. Add the salt.
Bring to a boil over high heat, then reduce the heat to maintain a simmer. Cook until the farro is as tender as you like, starting at about 25 minutes for semi-pearled and up to an hour for whole farro.
Meanwhile, heat the olive oil in a 12-inch skillet over medium-high heat.
Add the onion or shallot, mushrooms, and garlic and cook, stirring occasionally, until the onion is soft and the mushrooms have reduced substantially in volume, about 7 minutes.
Add the broccoli florets, soy sauce, and water or broth to the pan.
Cover and simmer until the broccoli is quite tender, 5 to 7 minutes more.
Remove the lid and cook one minute more to reduce any remaining liquid to just a few tablespoons.
Off the heat, add the drained farro and the parmesan cheese to the pan. Stir well and season with pepper. Serve warm.
