Bring a large pot of salted water to a boil. Add egg noodles and cook them according to package instructions, about 7-9 minutes, until al dente; drain and set aside.

In a large skillet, heat over medium heat. Add the ground beef, breaking it apart, and cook for about 6-8 minutes until uniformly brown; drain excess fat.

Reduce heat to medium-low, add butter, and melt completely. Sprinkle in the flour, whisking continuously for about 2 minutes to create a golden roux.

Gradually pour in the beef broth while whisking to prevent lumps. Bring to a simmer and cook for about 3-4 minutes until thickened.

Stir in the milk and cook for about 5-7 minutes until thick and smooth, stirring occasionally.

Incorporate garlic powder, onion powder, black pepper, and salt to taste; mix well until fully blended.

Lower the heat and mix the cooked noodles and browned beef into the skillet, stirring until well-coated with the sauce.

Remove from heat and stir in the sour cream until fully incorporated; serve hot garnished as desired.