Prep the vegetables: chop the onion, slice the carrots and celery, mince the garlic, dice the potatoes and zucchini, cut the green beans into 1-inch pieces, and shred the cabbage.
Heat the olive oil in a large pot over medium heat until shimmering, 1–2 minutes.
Add the onion, carrots, and celery; cook, stirring occasionally, until softened and lightly golden at the edges, 7–8 minutes.
Stir in the garlic and dried thyme; cook until fragrant, 30–60 seconds.
Add the canned diced tomatoes with their juices, vegetable broth, potatoes, and the bay leaf; bring to a boil over medium-high heat.
Reduce to a gentle simmer and cook for 10 minutes.
Add the green beans and cabbage; simmer until starting to soften, 10 minutes.
Stir in the zucchini, corn, and peas; simmer until all vegetables are tender, 5–8 minutes.
Stir in the kosher salt and black pepper; taste and adjust seasoning as needed. Discard the bay leaf.
Ladle into bowls and sprinkle with parsley (if using). Serve hot.