Dissolve 1½ tablespoons salt in 2 quarts cold water in large container. Add beans and soak at room temperature for at least 8 hours or up to 24 hours. Drain and rinse well.
Using highest sauté function, heat 2 tablespoons oil in Instant Pot until shimmering. Add carrots and celery and cook until softened, 5 to 7 minutes. Stir in cabbage, garlic, and pepper flakes and cook until cabbage starts to wilt, about 2 minutes. Stir in beans, 4 cups water, broth, V8 juice, Parmesan rind, if using, and salt.
Lock lid into place and close pressure-release valve. Select high pressure-cook function and cook for 30 minutes. Turn off Instant Pot and quick-release pressure. Carefully remove lid, allowing steam to escape away from you.
Discard Parmesan rind. Stir in zucchini and cook, using highest sauté function, until tender, about 5 minutes. Stir in basil and remaining 2 tablespoons oil, and season with salt and pepper to taste. Serve, passing extra oil and grated Parmesan separately.
