Whatever you do, do not throw that pan into the dishwasher! A lot of great flavor is locked on the bottom, waiting to be released.
We are making a red butter, or beurre rouge [burr roojh] sauce with the pan drippings. It is made the same as a classic beurre blanc [burr BLAHNGK]. One uses red wine (rouge) and the other uses white wine (blanc).
They are both made the same way using shallots, vinegar, wine, and cold butter. For this beurre rouge, substitute Madeira (a dark, strong wine) for the red wine. That makes the sauce stronger, and a better match for steak.
As soon as the steaks are done, lower the heat to medium, wait two minutes, and then add the shallots, see Step 1.
Add the shallots before the wine, so they can brown (also called caramelizing). You are looking for maximum flavor to match-up with the robust steak. Caramelizing the shallots brings out that extra flavor.
Just as soon as the shallots have browned (1-2 minutes), de-glaze the pan by adding the Madeira and balsamic vinegar, see step 2. Stir and scrape the bottom of the pan to loosen up all that good stuff. That will give the sauce tons of flavor.
Cook and stir the sauce until it is reduced to half of what you started out with. One way to check this is to look for rings inside the pan, telling you where the level used to be. You can also repeatedly tip the pan, sending all the sauce to one side. Establish a mark and keep checking the level.
It is important to reduce all the way to half, because that is what concentrates the flavor. Now start whisking in cold butter, one tablespoon at a time, see Step 3. Stir slowly and steadily, waiting until one piece of butter has melted before adding the next.
This part takes a little patience. But it is also important in making sure the sauce develops the right (very smooth!) texture, see Step 4.
These butter sauces are delicate, so they do not hold long (10 to 15 minutes, tops). Immediately pour a little sauce over each steak, see Step 5. Then garnish with cracked pepper.
* I would like to give you nutritional information, but I am too embarrassed, with all that butter. I want you to try this sauce though, because it is truly a French classic. If you are concerned about the fat, one to two tablespoons is all you use. And that little bit is not gonna hurt your diet.