Filet mignon with sauce Bernaise

Filet mignon, one of the most coveted pieces of meat, is awesomely tender, but low on flavor. That's probably why you see it served with sauce just about everywhere you go. Almost uniformly, the sauce is based on some fat emulsion because fat provides an irreplacable combination of flavor and mouthfeel.

Filet mignon with sauce Bernaise

Bernaise sauce is an augmentation of Hollandaise sauce adding shallot, herbs like chervil and tarragon, white wine, and white wine vinegar. Hollandaise sauce, in its purest form, is an emulsion of butter and egg yolks. It's like mayonnaise made with butter instead of oil. The technique to make it is different because to get butter in liquid form, it takes heat, and heat scrambles eggs.

For the filet, dry well, lightly oil and season as you wish with dry ingredients. Salt and pepper are really all you need, but you can put other stuff on there.
Sear in a heavy-bottom pan over high heat, open your windows or turn on your hood ventilation system. My preference is rare to medium rare.
Take the filet out, set it aside and let it rest on a wire rack about 5-10 minutes, save the juice if there is any. This should be made to order, and will take about 10 minutes total, depending on whether you already have them seasoned and your pan is ready to go. The reason to rest meat on a rack (particularly with a temperature sensitive meat like filet) is to prevent steam from being trapped on one side (the down side on the plate) and either overcooking or cooking unevenly.

For the sauce, get your Hollandaise setup with a simmering sauce pan of water, ice bath in the sink, and a non-reactive mixing bowl, preferably steel or something that will cool quickly.
Mince 1 tbsp of shallot, put in a saucepan with 1/2 cup of white wine (dry preferable over sweet) and white wine vinegar. Reduce by at least 1/2. That's your augmentation, although I didn't have the herbs. Since I was serving with salad (and I didn't have chervil), I left it out.
Strain and add that to your melted butter (about 1.5 to 2 sticks, yeah, no joke) and keep it warm.
Take 3 egg yolks, a little salt, a little pepper, 1 tbsp of lemon juice +/- 1/2 tbsp of water and whisk in your steel bowl. Dice up a couple of tbsp of cold butter and add to the egg yolks. Put this over your simmering water and start whisking. If it gets too hot, take it off heat. If you don't use the double boiler techique, you could really get it too hot, and that's where the ice bath comes in handy to cool it quickly. Curiously, the melting butter can look a little like scrambled eggs, but don't be dissuaded- press on! When you're done with this part, you should have a nice sticky yellow goo at the bottom of your pan.

To this you'll emulsify the melted butter/shallot-wine-wine vinegar reduction, slowly at first (drop by drop) until you get it started, then faster towards the end until you get the consistency you want. The only thing I can say about the consistency is that you want smooth and creamy like a salad dressing as opposed to thick like mayo. Check the Julia Childs instructions on classic Hollandaise for full instructions including bail out tips if you screw it up.

A little time consuming, but the ingredients are pretty cheap. Done that way, it's worth about 20-30 bucks per plate at the restaurant if you can even find it.
Below I've served it with sweet potato gnocchi and a basic green salad with balsamic vinaigrette.

From Drop Box