Usually Bearnaise is served on steak or lamb (and it is also delicious with fries!) but being mainly pescatarians it was halibut steaks for us and it worked beautifully.
A few words of advice. Do be overly cautious about overcooking the yolk mixture; remove the double boiler bowl from the heat often because once you overcook the yolks, the sauce is ruined. You will have to start over. Believe me, this has happened to me with hollandaise sauce, and it is as frustrating as it sounds! But patience is a virtue and this sauce is worth the time!
Reread the recipe several times to understand the process. Don't be overwhelmed by the length of instructions, it is just helpful tips so that you will be successful on your first try.
Bearnaise Sauce on Halibut Steaks (from the New York Times)
1/4 cup white wine vinegar
1 small shallot, peeled and minced
1 tablespoon plus 1 teaspoon fresh tarragon leaves, chopped
couple grinds fresh pepper
2 egg yolks
12 tablespoons melted butter
Place vinegar, shallot, 1 tablespoon tarragon and pepper in small sauce pan and bring to a boil; reduce to simmer and cook until only a few tablespoons remain, about 7-9 minutes. Set aside
Create a double boiler by fitting a bowl in a sauce pan and heating water in the sauce pan to a boil. Very Important! Make sure the bowl does not touch the water! Remove the bowl from the sauce pan while heating the water and add reduced vinegar mixture to yolks, plus 1 tablespoon of cold water and whisk vigorously.
Turn heat under saucepan with water down to the barest simmer and place bowl with yolk mixture over simmering water. Whisking continuously, cook the mixture until yolks begin to thicken. This is very similar to making hollandaise sauce, except you need to cook the yolk mixture at least 5-7 minutes so that it thickens before adding in the melted butter. The volume of the mixture will nearly double and it will be very thick.
Slowly add in the melted butter, 1 tablespoon at a time, whisking to emulsify. Remove the bowl from the heat ever minute or so to ensure the yolk mixture doesn't over cook (it will start to look like cooked eggs!) Add salt and lemon juice to taste. If the sauce appears to thick, thin with a little water. Stir in the remaining tarragon leaves and serve immediately.