Bring a large saucepan of salted water to a boil. Add the faro and simmer uncovered for about 30 minutes until the farro is tender but still pleasantly chewy. Drain the farro, cover, and keep warm.
Meanwhile, trim the greens from the radishes and coarsely chop the greens. Cut the radishes into quarters or eighths (depending on how large they are) and set the radishes and greens aside separately.
In a large sauté pan over medium-high heat, melt the butter. Add the radishes in a single layer, with most of the cut sides down, and cook undisturbed for 4 to 5 minutes until the bottoms start to brown and caramelize. Give a stir, then add the broth, vinegar, salt, and pepper, and bring to a boil.
Reduce the heat, cover, and simmer for about 10 minutes until the radishes are tender. Stir in the radish greens and cook for about 3 minutes until wilted. Turn off the heat, add the farro, and toss to combine. Serve warm with a sprinkle of feta and parsley on top.