Heat olive oil in a large skillet over medium-high heat. Add ground beef and cook, breaking it up with a spoon, until browned.
Add chopped onion and minced garlic to the skillet and cook until softened, about 3-5 minutes.
Stir in sliced mushrooms and cook until they release their moisture and start to brown, about 5-7 minutes.
Sprinkle flour over the beef and vegetables and stir to coat. Cook for 1 minute.
Gradually pour in beef broth, stirring constantly to prevent lumps. Bring to a simmer and cook until the sauce has thickened slightly, about 5 minutes.
Remove from heat and stir in sour cream and Dijon mustard. Season with salt and pepper to taste.
Serve hot over egg noodles or rice.
Notes
For a richer flavor, add a splash of Worcestershire sauce to the sauce. Garnish with fresh parsley, if desired.