I start by adding the diced tomatoes, tomato paste, sun-dried tomato pesto, parmesan rind, vegetable stock, and water straight into the slow cooker. Then in go the carrots, celery, onion, garlic, oregano, rosemary, and bay leaves. Season with salt and pepper, give it a quick stir, and you're basically done with the hard part.
Cover the crockpot and set it to low for 6-8 hours or high for 3-4 hours. This is the stage where I usually walk away and let the vegetables and herbs slowly build all that deep, comforting flavor while I go about my day.
Once the base has simmered down, stir in the red kidney beans, great northern beans, zucchini, and pasta. Switch the cooker to high and let everything cook for another 20-25 minutes, just until the pasta turns tender.
In the last few minutes, add the chopped spinach and thawed green beans. Let them cook for about 5 more minutes, just enough to heat through and wilt slightly without turning mushy.
Ladle the soup into bowls while it's steaming hot, and finish each bowl with a generous sprinkle of freshly grated parmesan. I like to serve mine alongside toasted garlic bread for dipping.