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Heat oil in a large Dutch oven or large pot over medium-high heat. Add cabbage and leek; cook, stirring often, until softened but not browned, about 4 minutes. Add garlic; cook, stirring constantly, until fragrant, about 1 minute. Add broth, salt, beans and Parmesan rind, if using; increase heat to high and bring to a boil.
Reduce heat to low to maintain a low simmer; cover and cook, undisturbed, until the cabbage is tender, about 10 minutes. Remove from heat and stir in vinegar. Remove and discard Parmesan rind, if using. Divide the soup among 4 bowls, and top with pesto.