Heat the olive oil over medium in large pot. Add the onion and saute until tender and translucent, about 5 minutes. Add the garlic and sauté until fragrant, another minute or 2.
Add the beans, any quicker cooking vegetables (ie zucchini, bell peppers, or asparagus), and the uncooked pasta. Continue to cook at a high simmer until the pasta is al dente. Add more broth, as needed.
Add the greens and cooked meat/poultry/beans (if using) and cook just until heated through. Taste and add salt and black pepper to taste. The amount of salt will vary depending on the type of broth you use. Remove the Parmesan rind and bay leaves before serving.
Serve with freshly grated Parmesan cheese over the top.
If you have leftover cooked pasta, feel free to use that in place of the uncooked pasta and add it at the very end of cooking the soup. Figure you'll need about 2 cups of cooked pasta. You can also use leftover rice, barley, or other grains in place of pasta if you happen to have that on hand.