In a large Dutch oven, heat 2 tablespoons of olive oil over medium heat. Add 1 chopped onion and 3 thinly sliced garlic cloves. Sauté for about 4 minutes until the onion is translucent and fragrant.

Stir in 4 cups of chopped green cabbage, 1 teaspoon of dried oregano, and a pinch of black pepper. Cook for approximately 3 minutes, until the cabbage wilts slightly.

Pour in 4 cups of vegetable broth and add 1 can of rinsed cannellini beans. Bring to a rolling boil, then reduce to a gentle simmer for 8 minutes.

Whisk together 1/2 cup of grated Parmesan cheese, 1/4 cup of fresh lemon juice, and 1 beaten egg in a bowl. Gradually whisk in about 1 cup of hot broth from the pot.

Once the cabbage is tender, remove from heat and stir in the tempered egg mixture. Add 1/4 cup of chopped fresh dill, stirring to combine.

Ladle the soup into bowls, garnishing with additional dill and freshly cracked black pepper. Serve it alongside a slice of crusty bread.