Classic Sauce Bearnaise for Rib Eye Steaks

I'm grilling a couple X-large rib-eye steaks tonight. Both guys in my house like their steaks seasoned with salt & pepper and THAT'S IT- no fancy rubs or seasonings, no sauces, no nothing!  I might steal a little piece for myself (although I eat very little meat) and if I do, I'll have a little bearnaise sauce on the side:

Ingredients:

1/2 pound (2 sticks) unsalted butter

4 shallots (or white onions), finely chopped 2 tablespoons fresh tarragon leaves (or 1tsp. dried) 4 white peppercorns, crushed (or 1/4 tsp. ground white pepper) 1/4 cup white wine vinegar 1/4 cup dry white wine (or white cooking wine/non alcoholic)

4 large egg yolks, lightly beaten 1/4 teaspoon salt Pinch of cayenne, if desired

Heat the butter in a medium saucepan over medium heat just to melt. Boil shallots, tarragon, and peppercorns in vinegar and wine in a nonreactive medium-size saucepan over medium heat until reduced to about 1/4 cup. Strain into the top of a double boiler.

Whisk in the egg yolks. Place the top over the bottom of the double boiler containing simmering water. Make sure that the top of the water is below the bottom of the upper part of the double boiler. Whisk constantly. The SECOND that the yolk mixture begins to thicken slightly, remove the top of the double boiler from above the hot water and continue whisking. (IF NOT THE EGGS WILL COOK!!)

Turn off the heat. Add four ice cubes to the bottom of the double boiler to cool the hot water a little. Put the pan of yolks back above the hot water. Whisk in the melted butter, drizzling it in very slowly. If at any time the sauce looks as if it is about to break apart, remove the top and continue whisking to cool it down or whisk in 1 teaspoon cold water. With constant whisking, whisk in the salt and cayenne. When all the butter is incorporated, taste and add more salt or cayenne- if you want a little heat!

Serve slightly warm but NOT hot - extreme heat will make this delicate sauce separate/curdle.