In a Dutch oven, heat olive oil over medium heat. Add chopped onion and sliced garlic cloves, stirring until fragrant and soft, about 4 minutes.

Stir in chopped green cabbage, dried oregano, and ground pepper. Cook for about 3 minutes, allowing cabbage to wilt.

Pour in vegetable broth and add rinsed cannellini beans. Bring to a boil, then reduce to a simmer and cover for approximately 8 minutes.

While simmering, whisk together grated Parmesan cheese, lemon juice, and egg in a heatproof bowl. Gradually whisk in hot broth to temper the egg.

Remove from heat and stir in the tempered egg mixture, chopped fresh dill, and salt to taste. Mix well until combined.

Ladle into warm bowls, garnishing with extra dill and freshly ground pepper. Serve with crusty bread.