Heat 2 tablespoons of olive oil in a large Dutch oven over medium heat. Add 1 chopped onion and 3 thinly sliced garlic cloves. Sauté for about 4 minutes until the onion turns translucent and the garlic is fragrant, stirring frequently to prevent burning.

Stir in 4 cups of chopped green cabbage, 1 teaspoon of dried oregano, and a pinch of freshly ground black pepper. Continue to cook for an additional 3 minutes, allowing the cabbage to slightly soften.

Pour in 4 cups of reduced-sodium vegetable broth and add 1 can (15 oz) of rinsed cannellini beans. Increase the heat to bring to a gentle boil, then reduce it to a simmer. Cook for about 8 minutes, until the cabbage is tender.

In a heatproof bowl, whisk together 1/2 cup of grated Parmesan cheese, the juice of 1 large lemon, and 1 egg. Gradually temper the egg mixture by adding hot broth from the soup, whisking constantly.

Remove the soup from heat and gently stir in the tempered egg mixture until fully combined. Add a handful of chopped fresh dill and season it with salt to taste.

Ladle the soup into warm bowls and garnish with additional fresh dill and cracked black pepper. Enjoy with crusty bread.