Bring the chicken broth to a boil in a large saucepan over high heat. Add the farro and stir to combine. Reduce the heat to low and simmer the farro, covered, until tender, about 25 minutes. Drain farro and set aside in a large bowl.
Meanwhile, in a food processor combine the parsley, basil, thyme, and garlic. Pulse until the herbs are roughly chopped. Add the olive oil, vinegar, salt, and pepper. Pulse again until the herbs make a coarse mixture.
Toss the warm farro with the coarse pesto. Transfer to a serving bowl. Using a vegetable peeler on the cheese wedge to make about 1/2 cup of cheese shavings. Top the farro with the cheese shavings and serve.