Heat 2 tablespoons of olive oil in a large Dutch oven over medium heat. Add 1 chopped onion and 3 thinly sliced garlic cloves, sautéing until they become fragrant and the onion turns translucent, about 4 minutes.

Stir in 4 cups of chopped green cabbage, 1 teaspoon of dried oregano, and ½ teaspoon of ground pepper. Cook for an additional 3 minutes until the cabbage begins to wilt.

Pour in 6 cups of vegetable broth and add 1 can (15 ounces) of rinsed cannellini beans. Bring to a gentle boil, then reduce heat and simmer for about 8 minutes.

Whisk together ½ cup of grated Parmesan cheese, juice of 1 lemon, and 1 large egg in a heatproof bowl. Gradually whisk in about 1 cup of the hot soup broth to temper the egg.

Remove from heat and stir the tempered egg mixture back into the soup along with ¼ cup of chopped fresh dill and salt to taste.

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