Melt 3 Tbsp of butter in a large skillet on medium heat. Increase the heat to high/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 shallots. Cook the shallots 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 Tbsp of butter. Increase heat to medium high and add the mushrooms. Cook, stirring occasionally for about 4 minutes. While cooking, sprinkle the nutmeg and the tarragon on the mushrooms.
Reduce the heat to low and add the sour cream to the mushrooms. You may want to add a tablespoon or two of water to thin the sauce (or not). Mix in the sour cream thoroughly. Do not let it come to a simmer or boil or the sour cream will curdle. Stir in the beef and shallots. Add salt and pepper to taste.