Place farro in a strainer. Rinse with cold water; set aside.
In a 4- to 5-quart Dutch oven heat 2 tablespoons butter and the oil. Add mushrooms and onion; cook and stir until tender. Stir in farro.
Slowly add white wine to farro mixture, stirring constantly. Continue to cook and stir over medium heat until wine is absorbed. Add 1/2 cup of the warm broth. Continue to cook and stir constantly until broth is absorbed. Add the remaining broth, 1/2 cup at a time, stirring constantly until broth has been absorbed and the farro is tender to the bite but still retains some chewiness. (This should take about 30 minutes total.)
Season farro to taste with salt and pepper. Remove from heat. Add cheese and 2 tablespoons butter, stirring until combined. Stir in the 1/3 cup parsley. Serve in individual bowls topped with hazelnuts and additional snipped parsley.