Bring a large pot of lightly salted water to a rolling boil. Cook the farro at a boil until tender, about 25 minutes.
Drain and set aside.
While the farro cooks, heat the olive oil in a large skillet over medium heat; cook the cauliflower and onion in the hot oil until the cauliflower begins to soften and the onion starts to become clear, 7 to 10 minutes. Stir the carrot, celery, and salt into the cauliflower mixture; continue cooking and stirring until the cauliflower is completely tender.
Combine the farro and the cauliflower mixture in a large bowl; stir to mix evenly.