1 cup dried large lima beans
2 bunches dandelion greens, Swiss chard, or mustard greens, stems removed, leaves cut into 2-inch pieces
4 tablespoons extra-virgin olive oil, divided
2 celery stalks, finely chopped
2 carrots, peeled, finely chopped
1 large onion, finely chopped
2 quarts chicken broth (or 1 qt water and 1 qt broth)
2 large heirloom tomatoes diced
1/2 cup freshly grated Parmesan cheese
Place beans in large bowl. Pour enough cold water over to cover; let soak overnight.
Drain beans; place in heavy large pot and add enough water to cover by 2 inches. Bring to boil. Reduce heat to medium-low and simmer until beans are just tender, about 45 minutes. Add greens to pot; cook until tender, 4 to 5 minutes. Drain; set aside.
Heat 3 tablespoons oil in same pot over medium heat. Add celery, carrots, and onion. Sauté until onion is translucent, about 6 minutes. Add broth, tomatoes, and bean mixture. Reduce heat to low. Simmer 20 minutes to allow flavors to blend. Cover and let soup rest 15 minutes. Ladle soup into bowls. Sprinkle with cheese and drizzle with remaining 1 tablespoon oil.