Preheat oven to 350�F.
Arrange beets in single layer in 8 x 8 x 2-inch baking dish. Drizzle with vegetable oil. Cover with foil and roast until beets are tender, about 45 minutes. Cool. Trim beets; peel.
DO AHEAD: Can be made 1 day ahead. Cover; chill.
Cook farro in large saucepan of boiling salted water until tender, stirring occasionally, about 20 minutes. Drain. Transfer to large bowl.
Stir 2 tablespoons olive oil, 1 tablespoon vinegar, and garlic into hot farro. Cool to room temperature.
Cut each beet into 6 to 8 wedges. Add beets, radicchio, onion, and parsley to farro; toss to incorporate evenly.
DO AHEAD: Can be made 1 day ahead. Cover and chill.
Whisk 2 tablespoons olive oil and 3 tablespoons vinegar in small bowl. Drizzle over salad. Add feta cheese; toss to coat.
This recipe calls for semipearled farro, a version of the grain that doesn�t require soaking before being cooked. If you're using regular farro, it will need to soak overnight. Farro is available at specialty foods stores, natural foods stores, and Italian markets.