Place all ingredients except for peas and corn in a slow cooker. Gently stir to combine. Cover and cook on LOW for 6-8 hours or on HIGH for 2-4 hours (or until potatoes and other vegetables are tender).
Stir in the frozen peas and corn during the final 30 minutes of cooking time.
Remove bay leaves. Season with additional salt and pepper, to taste. Ladle into bowls and serve!
ALTERNATE STOVETOP DIRECTIONS
Heat about 1 tablespoon of olive oil in a large pot over medium-high heat. Add the onions, carrots, and celery and sauté 4 minutes. Add the garlic and sauté 1 more minute. Stir in broth, tomatoes, potatoes, zucchini, tomato paste, parsley, bay leaves, thyme, salt and pepper. Bring to a boil, then add green beans. Reduce heat to medium-low, cover, and simmer until potatoes are almost tender, about 20 - 30 minutes. Add corn and peas and cook 5 minutes longer.
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Notes
Every slow cooker runs at a slightly different temperature (which is why the recipe gives you general time ranges, rather than exact times). Since my slow cooker tends to cook at a relatively high temperature, I find that the meal is best when cooked on HIGH for about 2 hours or on LOW for about 4-5 hours. Just get familiar with your pot and adjust accordingly. You'll know the soup is done as soon as the potatoes (and other veggies) are tender.
You do not need to thaw the peas or corn before adding them directly to the soup. They will thaw almost immediately when they hit the hot broth.
Fresh herbs add great flavor to this old-fashioned soup when they're available. If you don't have access to the fresh version, the dried herbs are fine, too!
A squeeze of fresh lemon juice, lime juice, or a splash of vinegar at the very end is a nice, bright addition.
Garnish each bowl with freshly-grated Parmesan cheese, chopped fresh parsley, cilantro, thyme, or a dollop of sour cream for a delicious finishing touch!