Add the base to the slow cooker.
Combine diced tomatoes, tomato paste, vegan sun-dried tomato pesto, vegetable stock, water, carrots, celery, onions, garlic, oregano, rosemary, bay leaves, and a pinch of salt and pepper into the slow cooker. Stir gently.
Cook low and slow.
Cover and cook on high for about 4 hours 25 minutes (you requested this timing). If you prefer longer and gentler cooking, use low for 6–8 hours — but you already asked for 4:25, so high it is!
Add beans, zucchini, and pasta.
About 25 minutes before the end of cooking, stir in the red kidney beans, great northern beans, zucchini, and ditalini pasta. Cover and cook on high until the pasta becomes tender (~20–25 minutes).
Finish with greens.
Stir in the chopped baby spinach and thawed green beans, then cook 4–5 minutes more until the spinach wilts and the green beans heat through.
Season and serve.
Remove the bay leaves and rosemary sprig if used fresh. Taste and adjust salt and pepper. Serve hot with nutritional yeast or vegan Parmesan on top and a side of garlic toast.
Pro tip: If you like a slightly creamier broth, blend 1 cup of the beans with a ladle of broth in a blender and stir back into the pot before adding the pasta. It thickens naturally without dairy.