Set oven to 400 degrees.
Wash and cut turnips in half. Rub with olive oil and wrap in aluminum foil. Peel sweet potatoes and rub with olive oil and cover with aluminum foil. Put both into the oven until easily pierced with a fork (about 45 minutes).
In a large pot, heat oil and add onion and garlic and sauté until translucent. Add chicken broth, water, chicken breasts, brown rice (if uncooked), salt, and pepper and bring to a boil. Reduce heat to low and simmer 20-25 minutes. Remove chicken breasts and shred off the meat with a fork.
Preheat oven to 425 degrees. On a large rimmed baking sheet, toss the carrots and parsnips with the butter, oil, and honey. Spread the vegetables in a single layer and season with salt and pepper. Roast the carrots and parsnips for about 35 minutes, or until tender.