Tip:If you made the chicken broth yourself, use the cooked meat from that
bird; otherwise you can use the meat from a store-bought rotisserie
Heat the oil over medium-high heat in a large (at least 8-quart), heavy-duty pot or Dutch oven. Add the fennel, leek, and 1/2 Tbs. salt. Cook, stirring occasionally, until the vegetables are softened and lightly browned in places, 4 to 6 minutes. Add the rosemary and cook, stirring, until fragrant, 30 seconds.
Add the broth and bring to a boil. Reduce to a simmer and cook, stirring, until the vegetables are completely tender, 20 to 30 minutes.
Stir in the shredded chicken, farro, beans, and escarole. Simmer, stirring occasionally, until all are tender and the flavors meld, 5 to 10 minutes.
Stir in 1 tsp. of the vinegar. Taste, and add more vinegar 1 tsp. at a time up to 2 Tbs. Season with salt and pepper to taste and garnish each bowl with a 1 Tbs. of the grated cheese, if you like.