Bring a large pot of salted water to a rolling boil. Add the egg noodles and cook according to package directions until just al dente. Drain and set aside.

While the noodles cook, heat a large skillet over medium heat. Add the ground beef and break it apart with a spoon. Cook until no pink remains, about 6 to 8 minutes. Drain excess fat and transfer the beef to a plate.

Return the skillet to medium heat and melt the butter. Sprinkle in the flour and whisk without stopping for about 2 minutes to cook the flour and create a roux.

Slowly pour in the beef broth while whisking constantly to prevent lumps. Keep whisking until the mixture thickens, about 3 to 4 minutes.

Gradually whisk in the milk and continue stirring until the sauce thickens again, about 5 to 7 minutes. Stir in garlic powder, onion powder, black pepper, and salt. Taste and adjust seasoning.

Lower the heat to low. Add the cooked egg noodles and the browned ground beef back into the skillet. Stir until everything is heated through and evenly coated with sauce.

Remove the pan from heat. Gently fold in the sour cream until the sauce is smooth and creamy. Serve immediately with steamed vegetables or toast.