Heat 2 tablespoons of oil in a heavy large skillet over medium heat. Add the shallots and saute until tender, about 2 minutes. Add the radicchio and saute until wilted, about 5 minutes. Add the beans and broth, and cook until the beans are heated through, stirring often, about 5 minutes. Season the radicchio mixture, to taste, with salt and pepper.
Meanwhile, heat 3 tablespoons of oil in a 14-inch (or 2 smaller) nonstick frying pan
over medium-high heat. Sprinkle the fillets
with salt and pepper. Dredge
the fillets in flour to coat completely. Shake of the excess flour and fry 3 fillets in each pan until they are golden brown and just cooked through, about 3 minutes per side.
Spoon the radicchio
mixture over the center of the plates. Top with the fillets. Drizzle
the vinaigrette over and serve immediately.