Run baking dish under broiler until top browns, checking every 30 seconds.
Combine all the remaining ingredients, and pour into baking dish; cover.
Cover baking dish with a sheet of parchment paper, and bake for 45 minutes.
Transfer fish to baking dish, cover again and return to oven.
Cover baking dish with foil, place in oven and bake 3 hours.
Spread plums in baking dish and dot with remaining butter.
Spread potatoes in baking dish and smooth the top.
Pour off duck fat from baking dish and reserve for another use.
Cover baking dish with lid or foil and bake for 30 minutes.
Place baking dish over high heat to bring wine mixture to a full boil.