Boil egg noodles in salted water according to package directions until al dente; drain and set aside.

In a large skillet over medium heat, brown ground beef until no longer pink; drain excess fat.

Add butter to the skillet until melted, then whisk in flour for about two minutes to create a roux.

Gradually stir in beef broth while whisking continuously until thickened, about four minutes.

Slowly add milk and continue whisking until smooth; simmer for five to seven minutes.

Season with garlic powder, onion powder, salt, and pepper.

Fold in cooked egg noodles and sour cream until well combined; heat through before serving.