In a large pot, heat 2 tablespoons of extra-virgin olive oil over medium heat. Once hot, add 1 chopped medium onion and sauté for 4–5 minutes until it turns translucent and fragrant.

Next, stir in 6 thinly sliced garlic cloves, cooking for about 1 minute until they are fragrant and golden. Then, add 6 cups of chopped green cabbage, stirring well. Sauté for 5–6 minutes until the cabbage softens.

Add 1 can of rinsed low-sodium cannellini beans to the pot, followed by 6 cups of low-sodium vegetable or chicken broth. Bring to a rapid boil, then reduce heat to low and simmer uncovered for 10 minutes.

Whisk together 1/4 cup of freshly grated Parmesan cheese, 1 tablespoon of fresh lemon juice, 1 large egg, 1/4 teaspoon of ground pepper, and 1/4 teaspoon of salt in a separate bowl.

Once the soup has simmered, remove it from heat to prevent curdling. Slowly drizzle the egg mixture into the soup while stirring constantly with a wooden spoon.

Return the pot to low heat, stirring the soup for an additional 2–3 minutes until it thickens slightly and everything is heated through.

Ladle the soup into bowls and serve immediately. Garnish with additional freshly grated Parmesan if desired.