Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 5 minutes. Stir in the garlic and cook for 1 minute more.
Add the beets and celery root to the pot. Cook for 5 minutes, stirring occasionally to coat the vegetables.
Stir in the farro, vegetable broth, balsamic vinegar, thyme, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 35 to 40 minutes until the beets and celery root are tender and the farro is cooked through.
Ladle the stew into bowls and top each serving with chopped parsley.