If you haven't already done so, start to prepare your egg noodles or mashed potatoes before you start your sauce.
Remove the meat and onions from the short ribs (you can discard the bones and fat) to a plate and the broth (carefully!) to a bowl (or jar) to save. Depending on how much fat is on your short ribs you may want to skim some of the fat off of your liquid before adding it to your sauce.
Note: depending on how much fat is on your short ribs you may want to skim some of the fat off of your liquid before adding it to your sauce.
Heat the now empty pan on the stovetop on medium-high heat, and add the mushrooms (yes, without any butter or oil!).
Cook the mushrooms for about five minutes without oil or salt, stirring occasionally until they are caramelized and start to sweat. If you allow them to sit undisturbed for some time, they will caramelize better. After they have caramelized, add 1/2 teaspoon pepper and 1 teaspoon salt. Remove from the heat and place on the plate with the short ribs.
Add 1/2 cup of chicken broth to the pot and scrape up any bits on the bottom (deglaze). Add ½ cup of the liquid from the short rib pot.
Bring the liquid to a boil and reduce the heat to a simmer for about 3-5 minutes, it will reduce slightly.
Taste the sauce and see if you prefer to have it richer or if it is too rich. If you feel the sauce is already plenty rich, use chicken broth for the next step. Otherwise use the rest of the broth from the short ribs or additional white wine.
Add an additional 1 cup of liquid (see note above) and let gently boil for an additional 3-5 minutes. If it is too rich or already too fatty add 1 cup of chicken broth, instead, and do the same.
Turn the heat to low, stir in the milk/sour cream, mushrooms, onions from the short ribs (if you like) and gently heat. Do not let boil.
In a bowl, add an egg yolk (just the yolk). While whisking (a fork works fine), add 2 tablespoons of the sauce and whisk well. Add another 4 more tablespoons and whisk well. Pour the egg mixture back into the sauce, while whisking. Let it simmer for about 2 minutes and thicken. See note below if you find your sauce isn’t the thickness you like.
Add the meat and onions (if you like) and stir gently.
Serve over egg noodles or mashed potatoes with a bit of fresh parsley on top..