Put all the vegetables except the tomatoes in a large pan with the olive oil and sweat over a medium flame for 10 minutes. Add the tomato and broth, then simmer until the vegetables are very tender, about 40 minutes. The soup can be held at this point, as the skate is only poached in it just before serving.
Bring the minestrone back to the boil (if left to cool), and check the seasoning. Drop the skate bits in and stir gently. Simmer for 5 minutes then serve with the rouille, crostini and Parmesan separately like a soupe de poissons.