Combine the broth, farro, mushrooms, leeks, Parmesan rind, bay leaf, nutmeg, 1¼ teaspoons salt, and ¼ teaspoon pepper in a 4- to 6-quart slow cooker. Top with the chicken.
Cover and cook until the chicken is tender, on low for 4 to 4 ½ hours or on high for 3 to 3 ½ hours (this will shorten total recipe time).
Discard the Parmesan rind and bay leaf. Using 2 forks, shred the chicken into large pieces. Stir in the butter and grated Parmesan.
Sprinkle the risotto with the parsley and serve with additional grated Parmesan.