In a large pot, heat olive oil over medium heat until shimmering. Add chopped onion and sliced garlic cloves, cooking until the onion is translucent and fragrant, about 4 minutes.

Stir in chopped green cabbage, dried oregano, and ground pepper. Cook for about 3 minutes, stirring frequently, until the cabbage begins to soften.

Pour in vegetable broth and add rinsed cannellini beans. Bring to a boil, then reduce heat to a simmer, cover, and cook for about 8 minutes until cabbage is tender.

In a separate bowl, whisk together grated Parmesan cheese, lemon juice, and an egg until smooth. Gradually mix in hot broth from the soup while whisking continuously.

Remove the pot from heat and gently stir in the tempered egg mixture and chopped dill. Mix carefully to combine.

Ladle the soup into bowls and garnish with additional dill and a sprinkle of freshly ground black pepper. Serve warm.