Melt butter in a small heavy saucepan over medium-high heat.
Stir in minced shallots and saute until shallots are tender.
Add 1 cup white wine.
Slowly boil the wine, uncovered, approximately 15 minutes, to reduce the wine to 1/2 cup.
When wine is reduced, add the cream and reduce the sauce again for approximately 15 minutes, uncovered, until it reaches a scant 2 cups.
The finished sauce should have a smooth, fairly thick consistency.
Stir the sauce often during the reduction process to prevent scorching.
Add dill, salt, and white pepper.
Keep warm.
While sauce is reducing, preheat oven to 350 degrees and prepare the fish.
Lay scrod fillets in a buttered baking dish.
Pour over 1/2 cup white wine, sprinkle with salt and white pepper to taste.
Cover fish loosely with tinfoil and bake approximately 15 minutes, or until fish flakes (proof that it is cooked through).
Do not overbake or scrod will loose its delicate texture.
Remove baked scrod from wine and place on warm plates.
Coat lightly with the dill sauce.