How to Make It
Preheat oven to 400°F. Lightly coat a 2-quart glass or ceramic baking dish with cooking spray. Cook farro according to package directions to yield about 4 cups; drain and set aside.
While farro cooks, melt butter in a large skillet over medium-high. Add mushrooms; cook, stirring occasionally, until lightly browned, 6 to 8 minutes. Add carrots, sage, and garlic; cook, stirring occasionally, until tender, 5 to 6 minutes. Stir in miso; cook, stirring constantly, 1 minute. Add stock; simmer until liquid is reduced by half, about 4 minutes. Remove from heat; cool slightly.
Combine cooked farro, mushroom mixture, cheese, vinegar, pepper, and salt in a large bowl. Spoon mixture into prepared baking dish. Bake at 400°F until top is lightly toasted, about 20 minutes.