Heat olive oil over medium heat in a large Dutch oven until shimmering. Add chopped onion and sliced garlic, cooking until the onion is soft, about 4 minutes.

Add chopped cabbage, oregano, and ground pepper. Stir well and cook for another 3 minutes until cabbage is tender.

Pour in vegetable broth and add rinsed cannellini beans. Increase heat to a gentle boil, then reduce to simmer for about 8 minutes.

In a separate bowl, whisk together grated Parmesan, lemon juice, and egg. Temper the egg by slowly adding hot broth while whisking.

Remove pot from heat and stir in the tempered egg mixture, chopped dill, and salt. Stir gently to combine.

Ladle soup into bowls, garnishing with additional dill and black pepper. Serve alongside crusty bread.