Bring a large saucepan of salted water to a boil. Add farro and cook until tender, about 30 minutes; drain and return to pot.
Meanwhile, in a large skillet, heat oil over medium-high. Add mushrooms, shallots, celery, ham, and 1 tablespoon sage; season with salt and pepper. Cook until celery is crisp-tender, 2 to 4 minutes.
Add wine and cook until evaporated, 3 to 5 minutes. Add 1 tablespoon sage and vegetable mixture to farro; toss to combine. Serve garnished with extra sage leaves.