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

Add 4 cups of chopped green cabbage, 1 teaspoon of dried oregano, and a sprinkle of black pepper. Cook for another 3 to 4 minutes until the cabbage starts to soften.

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

In a heatproof bowl, whisk together ½ cup of grated Parmesan cheese, the juice of 1 lemon, and 1 large egg until smooth. Slowly drizzle in about ½ cup of hot broth while whisking constantly.

Remove the pot from heat and stir in the tempered egg mixture along with ¼ cup of freshly chopped dill. Season with salt to taste and mix until well incorporated.

Ladle the warm soup into bowls, garnishing each with additional dill and a sprinkle of black pepper. Serve immediately.