Season the beef strips generously with salt and pepper. Heat oil in a large skillet over medium-high heat.
Working in batches, brown the beef strips for 2-3 minutes per side. Remove and set aside.
In the same pan, melt butter and add mushrooms. Cook until golden brown, about 5 minutes.
Add onions and garlic, cooking until softened, about 3-4 minutes.
Sprinkle flour over the vegetables and stir for 1 minute.
Gradually add beef broth, stirring constantly to prevent lumps.
Bring to a simmer and cook until sauce thickens, about 5 minutes.
Meanwhile, cook egg noodles according to package instructions.
Reduce heat to low and stir in sour cream and Dijon mustard.
Return beef to the pan and heat through, about 2-3 minutes.
Serve over hot egg noodles and garnish with parsley if desired.