Bring a large pot of water to a boil. Meanwhile, cut stems from Swiss chard leaves by making a V-shaped cut into each leaf around the stem. Finely chop stems, cut leaves into ribbons, and set both aside separately.
Boil tomatoes for 30 seconds. Lift out with a slotted spoon and rinse under very cold water. Remove the skin with a paring knife or vegetable peeler. Cut tomatoes into quarters, remove seeds, and chop. Set tomatoes aside.
Whirl half of cannellini beans with 1/2 cup water in a blender until smooth. Set bean purée aside.
Cook olive oil and garlic in a large pot over medium-high heat until fragrant, about 2 minutes. Add carrots, zucchini, reserved chopped chard stems, and salt. Cook, stirring, until stems are tender, about 5 minutes. Add white wine and cabbage. Cook, stirring, until cabbage wilts, 2 to 3 minutes.
Add reserved chard leaves, remaining cannellini beans, the chopped tomatoes, bean purée, chickpeas, parmesan rind, and broth. Bring to a boil, then reduce heat to maintain a steady simmer. Cook until all vegetables are tender and flavors blend, about 15 minutes. Remove parmesan rind. Serve soup hot, topped with shredded parmesan.
Note: Nutritional analysis is per serving.