Cook the farro in a pot of salted boiling water until al dente, about 15 minutes. Drain and set aside.
Heat the olive oil in a saute pan set over medium-high heat. Add the brussels sprouts and sprinkle with the salt. Cook the brussels sprouts (without stirring) until the edges begin to brown, about 2 minutes. Stir the brussels sprouts and cook for another 2 minutes until cooked but still firm. Stir in the balsamic vinegar.
Add the cooked farro and stir until heated through. Remove from heat and stir in the hazelnuts and dried cranberries. Top with the pieces of goat cheese and serve immediately.
Note: Look for farro in your grocery store near other grains like quinoa and rice.