Warm the oil in a 5-quart heavy-duty pot over medium-low heat. When it’s warm—not hot—add the carrots, celery, onion, garlic, and parsley. Cook, stirring often, until the onion is translucent, about 5 minutes. Add the potato and cook, stirring often, until it has begun to soften, about 5 minutes; turn the heat down if the vegetables begin to color.
Season the vegetables with 1 tsp. salt, then stir in the greens by the handful—it will seem like a lot, but they will cook down. Cover the pot and cook over low heat until the greens have started to wilt, about 3 minutes. Uncover and continue to cook, stirring occasionally, until the greens are completely wilted, about 3 minutes more.
Turn the heat up to medium high and add the broth, rice, and cheese rind, if using. Bring the soup to a boil. Turn the heat down to maintain a simmer and cook, uncovered, until the rice is very tender and has begun to split, 20 to 25 minutes. Season to taste with salt and pepper. Remove from the heat and stir in the basil. Let cool to warm or room temperature.
Serve the soup drizzled with extra-virgin olive oil.
nutrition information (per serving):
13, Fat Calories
110, Saturated Fat
9, Monounsaturated Fat
37, Polyunsaturated Fat
Photo: Scott Phillips