Prepare the beef - For cuts of beef that are especially thick, use a rolling pin or mallet to flatten the steak so that it is approximately 1/3-1/2-inch thick. Slice into thin strips and discard any excess fat. Sprinkle with salt and pepper, to season.
Brown the beef - Add 1 tablespoon of olive oil and one tablespoon of butter to a large heavy-bottomed skillet over high heat. Once the pan is nice and hot, add a single layer of beef to the skillet, allowing it to cook, untouched, for just 30 seconds. Immediately flip beef and allow to cook for an additional 30 seconds maximum. Transfer beef to a clean plate (do not worry if parts are still red or raw).
Repeat until all beef is browned - Repeat the process until all beef has been browned, adding additional olive oil and butter as needed.
Cook the onions and mushrooms - Reduce heat to medium-high. Add the remaining 3 tablespoons of butter and the onions to the skillet. Mix well to combine. Cook the onions, stirring often, for 3-4 minutes, or until onions soften and turn translucent. Add the garlic and cook for 1 minute, stirring continuously. Add the mushrooms and continue to cook until browned and golden, approximately 3 minutes.
Add the flour - Sprinkle the flour over the onions and mushrooms and continue to cook, stirring continuously, 1 minute.
Add the broth - Still stirring continuously, slowly add the beef broth to the onions and mushrooms. Once half the broth has been added, stir in the rest and mix well to combine.
Whisk in the Dijon mustard, Worcestershire sauce, and sour cream and bring to a simmer. Reduce heat too low and continue to simmer for 4-5 minutes, stirring frequently.
Return beef - Add the beef, with its juices, back to the pot and mix well to combine. Allow beef to simmer for 1-2 minutes before removing from heat.
Season and serve - Season with additional salt and pepper, to taste and season with fresh chopped parsley and cooked egg noodles, if desired.