How to Make It
Heat the oil in a large pot over medium-high heat. Add the onion, garlic, 1 teaspoon salt, and ½ teaspoon pepper. Cook, stirring occasionally, until the onion is tender, 8 to 10 minutes. Add the broth and tomatoes with their juices and bring to a boil. Add the barley, reduce heat, and simmer until the barley is tender, about 20 minutes.
Add the collards or kale and the beans and cook until the greens are wilted and the beans are heated through, 3 to 5 minutes. Stir in the Parmesan and ½ teaspoon each salt and pepper.
Serve the soup drizzled with olive oil and sprinkled with additional Parmesan.