Melt the butter in a Dutch oven set over medium-high heat. Add the garlic, onions and carrots and cook, stirring often, until the onion is translucent, about 5 minutes. Season lightly with salt and pepper.
Stir in the chicken broth, chard, pasta, green beans, oregano, pasta sauce, cannellini beans, squash, zucchini, 1 cup water, 2 teaspoons salt and several grinds of pepper. Bring to a simmer and cook until the pasta is cooked and the vegetables are tender, about 5 minutes.
Divide among 6 bowls and top with the torn basil and Parmesan.
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