Preheat oven to 400°F. Partially cook the squash by roasting in the oven on a sheet pan. Toss squash pieces in 1 tablespoon olive oil and roast about 15 minutes.
Bring 3 cups water to a boil in a medium sized saucepan with lid. Rinse the farro with water, drain and add to the pot with the salt. Cover the pot and bring back to boil then remove lid, lower the heat to maintain a gentle simmer, and cook until the farro is just tender, "al dente", about 15 minutes. Drain off water and set aside. (Will result in about 3 cups cooked farro.)
Heat the butter and olive oil in a large, deep sauté pan or dutch oven set over medium heat. Add the onions and sage and cook for 10 minutes, until the onions are soft and translucent.
Add the cooked farro and broth to the onions, and bring to a boil. Add the chestnuts and partially cooked squash, and stir to combine. Reduce heat to low, cover the pan leaving a small air gap, and cook at a slow simmer until most of the broth as been absorbed. Stir in the butter and season with salt and pepper.