For mushrooms: Heat olive oil in a large skillet over high heat. Add half the mushrooms and cook, stirring occasionally, until golden and tender, about 7 minutes. Season with coarse salt and freshly ground pepper and transfer to a bowl. Repeat for remaining mushrooms. Keep warm until ready to serve.
For stock: Combine stock ingredients in a 4-quart saucepan and bring to a boil over medium-high heat, about 8 minutes. Reduce heat and simmer 15 minutes. Reduce heat to the lowest setting to keep stock hot but not evaporating.
For risotto: In another 4-quart pot, heat the olive oil over medium heat. Cook, stirring, until onion is translucent, about 2 minutes. Add farro and cook, stirring, until just starting to turn translucent (farro will start making a clicking sound), 1 to 2 minutes. Reduce heat if onion begins to brown.
Pour wine into farro and onion mixture and cook, stirring, just until absorbed (farro should still be wet and glistening, not dry). Using a ladle, add 1/2 cup hot stock to the farro. Stir constantly with a wooden spoon, at a moderate speed, until about three-quarters of the liquid is absorbed (the mixture should be thick enough to hold a trail behind the spoon). Continue adding stock 1/2 cup at a time and stirring frequently until farro is tender but still firm to the bite and the liquid is creamy in consistency. As farro nears doneness, watch carefully and add smaller amounts of liquid to make sure it doesn't overcook (you may not need to use all the broth). The process should take 30 to 35 minutes total.
For finishing: Stir in butter until completely melted (this is called mounting), then stir in cheese and season with salt. Serve topped with mushrooms, parsley, and pepper, and serve immediately.