Add the zucchini, beans, carrots, onion, celery, potatoes, green beans, garlic, spices, salt and pepper, canned diced tomatoes, tomato paste, and vegetable stock to your slow cooker and stir well to combine. Depending on the size of your slow cooker and how thick you like your minestrone soup, add between 6 and 7 cups of stock (I usually add about 6 at first and sometimes add up to 1/2 cup more).