Step 1In a heavy soup pot, warm the olive oil over medium-low heat. Add the carrots, celery, onion and turnip, cover and cook until they have softened and become aromatic, about 20 minutes. Stir in the garlic and cook until fragrant, 2 or 3 minutes.
Step 2Add the mixed greens, a big handful at a time, stirring and giving them time to soften and shrink before adding the next handful.
Step 3When all of the greens have cooked, add 8 cups of water, one-half teaspoon salt, the rosemary and chickpeas. Bring to a simmer over medium-high heat; cover and lower the flame to maintain a simmer. Cook until the broth is deeply flavored, 45 minutes to 1 hour.
Step 4When ready to serve, stir in one-third cup Parmigiano-Reggiano and season to taste with salt and pepper. Arrange two toast slices in the bottom of each warm soup bowl and ladle the soup over the top. Sprinkle with more cheese to taste. Serve immediately, passing a bowl of cheese to be added at the table.