Heat oil in a dutch oven or a large soup pot.
Add onions and cook for 1 minute over medium-high heat.
Stir in prepared bell peppers, carrots, salt, and pepper; cook for 2 minutes.
Add garlic and parsley; cook for 20 seconds.
Stir in cabbage and cook for 4 minutes, or until starting to wilt.
Add tomato paste; stir until combined.
Add roasted tomatoes and Italian seasoning; mix to combine.
Stir in broth and add bay leaves; increase heat to High and bring to a boil.
Lower heat to a steady simmer; continue to cook for 7 minutes.
Stir in zucchini slices and broccoli florets; cook for 5 more minutes.
Remove from heat.
Taste for seasonings and adjust accordingly.
Remove bay leaves and discard.