How to Make It
In a large pot, melt the butter with the oil over moderate heat. Add the onion and cook, stirring occasionally, until golden, about 5 minutes. Add the garlic, carrots, celery, and potatoes and cook, stirring occasionally, for 5 minutes. Add the zucchini and cabbage and cook, stirring occasionally, for 5 minutes longer.
Add the broth, beans, tomato paste, and salt and bring to a simmer. Simmer, partially covered, until the vegetables are tender, about 18 minutes. Add the sole, pesto, and pepper and bring back to a simmer. Cook, uncovered, until the fish is just done, about 1 to 2 minutes more. To serve, ladle into bowls and pass more pesto if you like.
Fish Alternatives You can use any other member of the flounder family, such as sand dab or fluke, in place of the sole. Or try a firmer, white fish, such as cod, halibut, or monkfish. For these thicker fish, add another minute to the cooking time.