Combine farro, 3 cups water, and 3/4 teaspoon salt in a small saucepan over medium-low; cook, covered, 25 to 45 minutes until it is softened but still chewy.
Strain farro and place in a large bowl. Add remaining 1/2 teaspoon salt, olive oil, vinegar, greens, peas, carrots, onion, celery, and beet; stir gently to combine.
Top evenly with cheese and parsley. Drizzle more balsamic vinegar on top if desired.