Combine the beans and their liquid with the garlic, salt, thyme, basil, and 2 cups of water in a large saucepan and bring to a boil over high heat. Reduce the heat to low and simmer for 5 minutes to meld the flavors. Remove about 1 1/2 cups of the beans, returning any garlic or basil to the saucepan. Use an immersion blender to purée the remaining beans in the pot until smooth.
(Alternatively, let the soup cool slightly then transfer it to a blender or food processor and purée, holding the lid down tight so the hot liquid doesn't splatter out.) Stir in the reserved beans and cabbage and thin the soup with water if necessary. Cook the soup over medium heat until the cabbage wilts and is slightly tender, about 5 minutes.
Divide the soup evenly among four large soup plates or bowls, filling them to just below the rim. Drizzle each serving with high-quality olive oil and grate a thin layer of Parmesan cheese over them. Tear one slice of the prosciutto into a few pieces and rumple the pieces onto one bowl of soup; repeat with the remaining prosciutto slices.