Heat the olive oil over medium heat. Add the shallot and sauté until just translucent, about 2 minutes. Add the farro and stir to coat the grain kernels with the oil. Cook for 2 minutes, stirring frequently, to lightly toast the farro.
Add the white wine to deglaze the pan. Add the stock, ½ cup at a time, stirring continuously. Do not add more stock until the previous stock has been absorbed. Repeat until the farro is tender. You may not use all of the stock. The farro should be cooked but still have a bit of chew. Total cooking time is about 25 to 30 minutes.
While farro is cooking, sauté the mushrooms in the unsalted butter. At the end of cooking the farro, stir in half of the mushrooms, the corn and the goat cheese. The goat cheese should melt within the farro making the dish slightly creamy.
Divide among two plates. Top with the remaining sautéed mushrooms and garnish with the Parmesan cheese.