3 garlic cloves, coarsely chopped
3 Tbsp. extra-virgin olive oil, plus more for drizzling
1 large shallot, coarsely chopped
1 lb. mixed mushrooms (such as crimini, shiitake, oyster, and/or maitake), cut into bite-size pieces
Kosher salt, freshly ground pepper
1 oz. Parmesan, finely grated (about 1 cup), plus rind
⅔ cup semi-pearled farro
3 Tbsp. (or more) low-sodium soy sauce
4 celery stalks, thinly sliced, plus any leaves coarsely chopped
1 Tbsp. fresh lemon juice
Crusty bread (for serving)
Heat garlic and 3 Tbsp. oil in a large Dutch oven or other heavy pot over medium until oil around garlic is sizzling, about 1 minute. Add shallot and mushrooms, season with salt and pepper, and cook, stirring occasionally, until mushrooms are browned, 10–15 minutes. (Initially, pot will look dry, then very wet before mushrooms start to brown.)
Add Parmesan rind, farro, soy sauce, and 6 cups water to pot. Scrape up any browned bits stuck to bottom of pot, season with salt and pepper, and bring to a boil over medium-high. Reduce heat and simmer until farro is al dente, 15–20 minutes.
Add sliced celery to pot and simmer until slightly softened and bright green, about 3 minutes. Remove pot from heat; add lemon juice. Taste and season with salt and/or more soy sauce if needed.
Divide soup among bowls and top with finely grated Parmesan and celery leaves. Season with more pepper and drizzle with oil. Serve with bread alongside.