Cook farro according to package directions, adding ¼ tsp. salt to the cooking water. Transfer the cooked farro to a large bowl; set aside.
Meanwhile, heat 1½ Tbsp. oil in a large or extra-large skillet over medium-high heat. Add mushrooms; cook, stirring occasionally, until very brown, 10 to 14 minutes. Transfer to a small bowl; set aside.
Reduce heat to medium. Add the remaining 1½ Tbsp. oil, garlic, carrot, celery, onion, and bell pepper to the pan; cook, stirring frequently, until the vegetables are lightly browned, about 6 minutes. Stir in broth, fennel seeds, and crushed red pepper; cook until the vegetables are tender and the broth has almost evaporated, 1 to 2 minutes.
Stir the farro, mushrooms and vinegar into the vegetable mixture in the pan. Add sage, rosemary, pepper, and the remaining ½ tsp. salt. Cook until heated through, 1 to 2 minutes. Stir in parsley.
