Melt half of the butter in a skillet. Add the onion and cook over moderately low heat, stirring frequently, until softened, about 8 minutes. Add the farro and thyme and cook, stirring occasionally, until the farro is lightly toasted, about 3 minutes. Add the water and a pinch each of salt and pepper. Bring to a simmer, cover and cook over low heat until the water is absorbed and the farro is al dente, about 30 minutes. Discard the thyme.
Meanwhile, melt the remaining 3/4 tablespoon of butter in a medium skillet. Add the mushrooms and cook over moderate heat, stirring frequently, until softened, about 5 minutes. Add the mushrooms to the farro, season with salt and pepper and serve.
The farro can be refrigerated overnight; gently reheat with 1/2 cup of water before serving.