Skin the pompano fillets. Wash under cold running water. Season with salt and pepper on both sides. Dredge in flour.
Heat 2 ounces of the butter and oil in a large skillet and brown the fish. Turn the pompano and cook until the flesh is tender. Arrange the fillets on a serving platter. Keep hot.
Mango beurre blanc:
In a small heavy pan, boil the vinegar, wine and shallots until all liquid is reduced. Add the cream, and re-boil until completely reduced.
Whisk in the cold butter, a few pieces at the time. The sauce thickens and becomes creamy. Stir in the orange juice and mango puree.
do not overheat the sauce, as the sauce separates and loses its creamy texture. Season to taste with salt and pepper. Keep the sauce warm over a pan of warm water. Serve as soon as possible.