Steak Frites Part Un: the sauce

I was craving steak frites (steak & fries) the other day so I set out to make it for dinner. A little background information:

L'entrecĂ´te is a French cut of steak: the sirloin opposite the tenderloin. It's hard to find this exact cut of meat in America but it's comparable to a sirloin steak or strip steak. There are a bunch of restaurants, Le Relais de L'EntrecĂ´te and a chain Le Relais de Venise (there's a location in NYC and here's a yelp link for the one I visited in Paris), where they serve just steak frites and your only choices are the doneness of the meat (rare, medium, or well - nothing in between), beverage, and dessert. The steak frites at these restaurants are served with this amazing secret sauce and there seem to be many people out there who try and replicate it (from what I've learned on google).

Here is Part Un (1) of a series of posts: my version of the sauce, which isn't exactly the same, but comes pretty darn close.

Ingredients [makes enough for about 4 steaks, can be made 1 day ahead, refrigerated, and warmed before serving]:
1/2 tablespoon olive oil
1/2 shallot, finely diced
1 clove garlic, minced
1/2 cup chicken stock
1/2 teaspoon black pepper
1 tablespoon mustard
3 sprigs of tarragon
1 tablespoon red wine vinegar
1/2 teaspoon anchovy paste (or 1 anchovy)
1/2 teaspoon Worcestershire sauce
1/2 teaspoon salt
1 tablespoon butter
I made my own chicken stock using 2 cups of water, 1 garlic clove, and 3 wing tips (which I had leftover from making wings for the Super Bowl). I brought the ingredients to a boil in a small sauce pan, lowered the heat a bit to a simmer, and let the stock reduce until I had about 1/2 cup of stock.

I finely diced half a shallot. If you've never used shallots before, it's kind of like if garlic and sweet onion had a baby. It's has a milder flavor than onion but it's still v. flavorful. If you don't have shallots, you can use sweet onion.
I heated the olive oil in a small sauce pan and let the minced garlic and shallot sweat. Once the shallots started to turn translucent and lose some of its purple color, I added in the chicken stock and let the mixture warm up.
Tarragon is an herb v. commonly used by the French. It has a strong and distinctive flavor that's fragrant and sweet but it isn't overpowering and goes great with poultry. To use, strip off the leaves from the main stem. The main stem is too woody for this sauce. The photo below shows unstripped tarragon on the left and the naked woody stem on the right.
I added the tarragon, salt, pepper, anchovy paste, mustard, Worcestershire, and vinegar to a food processor and pulsed until the tarragon leaves started to break down. Then I added in the stock mixture and pulsed until it formed a smooth liquid. A blender will also work. At this point, you can sieve the sauce to get rid of any chunks but I don't mind a few leaves of tarragon in the sauce - I think it makes it look rustic and homemade.
Then I returned the sauce mixture to the saucepan and let it simmer for a few minutes to reduce the sauce. I knew it was ready when the color had darkened a bit and the sauce was thick enough to coat the back of a spoon. Then I added in the butter and stirred until it completely melted.
Coming up is Part Deux: the salad

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