Prepare all vegetables: Chop the onion, mince the garlic, and dice the carrots, celery, potatoes, and any other chosen vegetables.
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion, carrots, and celery. Sauté until softened, about 5-7 minutes.
Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Stir in the diced potatoes, assorted vegetables, canned tomatoes, vegetable stock, bay leaf, Italian seasoning, dried oregano, sweet smoked paprika, red pepper flakes (if using), salt, and black pepper.
Bring the soup to a boil, then reduce the heat to low, cover, and simmer for 20-30 minutes, or until all vegetables are tender.
If using, stir in the rinsed and drained canned beans or chickpeas during the last 5-10 minutes of simmering to heat through.
Remove and discard the bay leaf. Stir in the fresh parsley (and optional basil or thyme) and a squeeze of fresh lemon or lime juice (and optional white wine vinegar) for a brighter flavor.
Taste the soup and adjust seasonings as needed, adding more salt, pepper, or herbs if desired. Serve hot with optional crusty bread.