Melt 3 tablespoons of butter in a large skillet on medium heat. Increase the heat to med-high and add the strips of beef. You want to cook the beef quickly, browning on each side, so the temp needs to be high enough to brown the beef, but not so high as to burn the butter. You may need to work in batches. While cooking the beef, sprinkle with some salt and pepper. When both sides are browned, remove the beef to a bowl and set aside.
In the same pan, reduce the heat to medium and add the onions. Cook the onions for a minute or two, allowing them to soak up any meat drippings. Remove the shallots to the same bowl as the meat and set aside.
In the same pan, melt another 3 tablespoons of butter. Increase heat to medium high and add the mushrooms, cook stirring occasionally for about 4 minutes. Sprinkle with nutmeg and the tarragon.
Reduce heat to low and add the sour cream to the mushrooms, mix thoroughly. Do not let it come to a simmer or boil or the sour cream will curdle. Stir in the beef and onions. Add salt and pepper to taste. Serve immediately over egg noodles, fettuccine, potatoes, or rice.