Melt half the butter in a medium saucepan and cook the onions and carrots until softened, about 5 minutes. Sprinkle the vegetables with the flour and cook, stirring, for 1 minute. Stir in the white wine and bouquet garni, and bring to a boil. Reduce heat and simmer, covered, for 20 minutes. Preheat the oven to 425F. Season the whiting both inside and outside, and lay them in a large shallow ovenproof dish. Stir 1/2 cup of water into the white wine sauce. Remove the bouquet garni and discard. Pour the white wine sauce over the fish and bake for 15 minutes, then cover with a piece of aluminum foil. Continue baking for 20-30 minutes, basting every 10 minutes. Turn off the oven and leave the dish in the oven for 10 minutes longer. Before serving, dab the remaining butter over the fish.
