Hope this isn't too late. But I saw you have couple of response so... Anyway, here is also a good recipe from "The Joy of Cooking". (p.57) I happened to try it with grilled bule eye fillet tonight!!! I think if you like Bearnaise sauce, you should like this sauce as well.
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Beurre Blanc (White Butter Sauce) 1/2 cup

Said to have been invented either in the Anjou region of France or in the vicinty of Nantes, and popularized in Paris by a restaurateur named Mere Michel, beurre blanc is among the most refined of French sauces. The only real trick to making a perfect sauce is to whisk in th ebutter without letting it melt comepletely. Cutting the butter into small cubes helps, as does removing the simmering liquid from the heat and whisking it constantly. The addition of a bit of heavy cream is added insurance that the sauce will hold together. Beurre blanc can be flavored by substituting various stocks for all or part of the wine, by adding herbs or citrus zest, or by replacing all or part of the butter with a flavored butter. Beurre blanc is traditional with fish, especially shad, asparagus, artichokes, and leek, among other foods. Some chefs strain the beurre blanc before serving, but it is not essential.

Combine in a small skillet over medium heat and simmer, uncovered, until cooked down by 3-quarters:
6 T. dry white wine
2 T. white wine vinegar
3 T. minced shallots
Salt and ground white pepper to taste
Stir in:
1 T. heavy cream
REmove from the heat and add, whisking constantly, 1 piece at a time until the sauce is creamy and whitened:
8 T. (1 stick) cold butter, prefeerably unsalted, cut into at leaast 8 pieces

If you need a bit more heat to soften the butter, hold the pan briefly over very low heat. Never let the butter melt completely, or the sauce will separate. Strain through a fine-mesh sieve, if desired, season to taste and serve immediately.