Slice the sirloin against the grain and into thin strips. Dust with the flour to coat. Set aside.
Cook the egg noodles according to package directions. Drain well and set aside.
Heat the olive oil in a large heavy skillet over medium-high heat. Add the onions and mushrooms. Sauté until tender, about 7 minutes, then remove from the skillet and set aside.
Without cleaning the skillet, add the butter and let it melt over medium-high heat. Add the steak slices and cook until browned, about 4 to 5 minutes.
Return the onions and mushrooms to the skillet. Pour in the beef broth and Worcestershire sauce. Simmer until thickened, about 2 to 3 minutes.
Add the sour cream and Dijon and stir until incorporated. Add the cooked egg noodles, stir to combine, and then season to taste with salt and black pepper. Serve hot over egg noodles, mashed potatoes, or cooked rice.
