Cook the farro according to the package directions. Meanwhile, whisk together the oil, lemon juice, mustard, caraway seeds, 1 teaspoon salt, and ¼ teaspoon pepper in a bowl. Add the radishes, beets, and fennel. Let sit, stirring occasionally, until the vegetables are slightly softened, 10 to 15 minutes. Add the chives and cooked farro and toss to combine.
