Preheat the oven to 400°F (200°C). Arrange the cucumber and half of the herbs in a large ovenproof dish, preferably metal.
Place the fish on top, cover with the rest of the herbs, and pour over the wine.
Cover tightly with aluminum foil and bake in the oven for 10 to 14 minutes or until the fish flakes easily when poked with a fork. (The precise cooking time depends on the thickness of the oven proof dish and is longer for one made with porcelain or other glassware.)
Meanwhile, melt a small knob of butter in a small pot over medium high heat. Add shallots and sauté for 2 minutes, until shiny but not brown. Set aside.
When the fish is done, strain the cooking juices into the pot with the shallots using a fine sieve. Reduce by half and remove from the heat. Whisk in cold butter, little by little.
Whisk vigorously, until you have an emulsion. Add salt and pepper to taste. Remove and discard the herbs from the ovenproof dish, transfer fish and cucumber to plate and pour over the butter sauce.