Heat 3 tablespoons of the olive oil in a large pot or Dutch oven over medium heat.
Once the oil is glistening, add the shallots, sliced fennel, and ½ teaspoon of the salt.
Cook, stirring often, until the fennel is softened and golden, about 10 minutes.
Stir in the garlic, cabbage, and remaining 1 tablespoon of olive oil, and cook until cabbage is bright green, about 3 minutes.
Add the stock, beans, parmesan rind, if using, pepper and the remaining 1 teaspoon of salt.
Increase the heat to high and bring to a boil, then reduce the heat to a simmer.
Cook until the beans are tender and the parmesan rind is soft, about 10 minutes.
Stir in the lemon juice, lemon zest, parsley and dill.
Ladle the soup into bowls and serve topped with pepper, reserved fennel fronds, and dill.
