1Prepare the beef by slicing it into thin strips about 1/4 inch thick and 2-3 inches long, cutting against the grain for maximum tenderness. If the beef is difficult to slice thinly, partially freeze it for 30-60 minutes until firm but not solid. Pat the beef strips completely dry with paper towels - wet meat will steam instead of sear. Season generously with salt, pepper, and paprika. Slice the mushrooms about 1/4 inch thick. Dice the onion and mince the garlic. Take the sour cream out of the refrigerator to bring it to room temperature - cold sour cream is more likely to curdle when added to the hot sauce.
2Heat 1 tablespoon each of butter and olive oil in a large skillet over high heat until the butter foam subsides and the oil shimmers. Working in batches to avoid overcrowding, add the beef strips in a single layer. Sear without moving for about 1 minute until deeply browned on the bottom, then flip and sear the other side for another 30 seconds. The beef should be browned on the outside but still pink inside - it will finish cooking in the sauce later. Transfer to a plate. Repeat with remaining beef, adding more oil between batches if needed. Do not wipe out the pan - the browned bits (fond) add tremendous flavor.
3Reduce heat to medium-high and add another tablespoon of butter to the same pan. Add the sliced mushrooms in a single layer and cook without stirring for 2-3 minutes until browned on the bottom. Stir and continue cooking for another 3-4 minutes until the mushrooms are golden brown and have released and reabsorbed their moisture. Season lightly with salt. Transfer to the plate with the beef. Add the remaining tablespoon of butter, then add the diced onion. Cook for 4-5 minutes, stirring occasionally, until softened and lightly golden. Add the garlic and cook for 1 minute until fragrant.
4Sprinkle the flour over the onions and garlic. Stir constantly for 1-2 minutes to cook off the raw flour taste and create a roux. Pour in the wine or brandy, scraping up all the browned bits from the bottom of the pan with a wooden spoon. Let the alcohol simmer and reduce for 1-2 minutes until mostly evaporated. Add the beef broth, Worcestershire sauce, and Dijon mustard. Whisk to combine and bring to a simmer. Let the sauce cook for 3-4 minutes until it thickens enough to coat the back of a spoon.
5While the sauce simmers, cook the egg noodles in a large pot of salted boiling water according to package directions until al dente. Drain and toss with a small pat of butter to prevent sticking. Return the seared beef and mushrooms to the sauce, along with any accumulated juices. Stir gently and simmer for 1-2 minutes just to heat through - do not overcook or the beef will become tough. Remove the pan from heat completely.
6This is the crucial step: with the pan completely off the heat, stir in the room-temperature sour cream. The sour cream must never boil or it will curdle and become grainy. Stir gently until the sauce is smooth, creamy, and pale beige in color. If the sauce seems too thick, add a splash of beef broth. Taste and adjust seasoning - you may need more salt, pepper, or a touch more mustard for brightness. Serve the stroganoff immediately over the buttered egg noodles, garnished with fresh chopped parsley. Traditional Russian accompaniments include straw potatoes or rice, but egg noodles have become the American classic. For a more authentic presentation, serve with pommes allumettes (matchstick fries) on the side. Beef stroganoff does not reheat perfectly - the sour cream can separate - so it is best enjoyed fresh.