Place the farro in a large pot of cold water and bring to a boil. Simmer for 15 to 20 minutes to par-cook the farro, and then drain and set aside.
In a heavy-based pot, add the butter and oil. Add the mushrooms, garlic and shallots and saute until just tender, 3 to 5 minutes. Deglaze with the white wine. Add the drained farro and stir to combine. Add the chicken stock to the pot a little at a time, ensuring at each addition that the liquid has been completely absorbed by the farro. Keep stirring and adding the stock until the mixture is thick and creamy.
Add the sun-dried tomatoes. Season with salt and pepper, and then add the Parmesan, sour cream and parsley.