Place 3 cups of salted water in each of two large saucepans and bring them to a boil. Add the wheatberries to one saucepan, and the farro to the other and cook, uncovered, over low heat for approximately 45 minutes, or until they are soft. Drain and place them together in a large bowl.
Meanwhile, saute the red onion in 2 tablespoons of olive oil over medium-low heat until translucent, approximately 5 minutes. Turn off the heat and add 1/4 cup of olive oil, the balsamic vinegar, 1/2 teaspoon salt and 1/2 teaspoon pepper. Add the onions to the wheatberries and farro together with the scallions, red bell pepper, carrot and parsley and mix well.
Allow the salad to sit for at least 30 minutes for the wheatberries and farro to absorb the sauce. Season to taste and serve at room temperature.