Sauté the aromatics. Heat olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrots, and celery and cook for 6–8 minutes, stirring occasionally, until softened.
Add garlic and tomato paste. Stir in the garlic and tomato paste. Cook for 1–2 minutes, stirring constantly, until fragrant and slightly darkened.
Build the soup base. Add the chopped cabbage, diced tomatoes, vegetable broth, potatoes, white beans, thyme, bay leaves, salt, and pepper. Stir to combine.
Simmer. Bring the soup to a gentle boil, then reduce heat to low. Cover and simmer for 25–30 minutes, stirring occasionally, until the potatoes are fork-tender and the cabbage is soft.
Finish and season. Remove bay leaves. Stir in lemon juice (if using) and chopped parsley. Taste and adjust seasoning with additional salt and pepper as needed.
Serve. Serve hot with crusty bread, garlic toast, or a simple side salad.