Trim the broccoli rabe, removing any discolored leaves, then thinly slice. To reduce the bitterness, place the greens in a bowl with cold water to cover and change the water a few times over the course of 2 hours.
In a saucepan, bring the broth to a boil. Add the rice and greens, cover, reduce the heat to medium-low, and simmer until the rice is tender, about 20 minutes. Season with sal