Place beets in a large saucepan and cover with water. Add 3/4 tsp salt and bring to a boil. Reduce to a simmer, cover, and cook until beets are tender, about 45 minutes. Remove from heat, and rinse beets with cold water. Rub skins off beets, trim ends, and cut into 1/4-inch pieces.
While the beets cook, bring 2 quarts water and 1 tsp salt to a boil. Add 1 cup farro and reduce heat to a medium low. Simmer until farro is tender, about 30 minutes. Drain excess water and add cooked farro to a serving bowl.
While the farro and beets cook, whisk together dressing ingredients. Add to farro in serving bowl while still warm; toss to coat.
Assemble the salad: Add the beets and chickpeas to the farro. Toss to combine. Serve at room temperature or refrigerate and served cold. Can be made 1 day in advance of serving; toss before serving.
