Bring a large pot of salted water to a boil and cook the egg noodles according to the package directions. For the best texture, cook them for about 2 minutes less than the instructions suggest so they remain slightly firm. Drain the noodles but do not rinse them.

While the noodles are boiling, heat a large skillet over medium heat. Add the ground beef and cook, breaking it up with a wooden spoon, until it is fully browned and no pink remains. Drain any excess grease and set the beef aside on a plate.

In the same skillet, melt the butter over medium heat. Once melted, sprinkle in the flour and whisk constantly for about 2 minutes to create a smooth roux.

Slowly pour the beef broth into the flour mixture, whisking continuously to ensure there are no lumps. Continue to stir until the sauce begins to thicken.

Gradually whisk in the milk and continue simmering over medium heat. Stir frequently until the sauce thickens again into a creamy consistency.

Stir in the garlic powder, onion powder, salt, and black pepper, ensuring the seasonings are evenly distributed throughout the sauce.

Reduce the heat to low. Add the cooked egg noodles and the browned ground beef back into the skillet. Toss everything together until the noodles and meat are thoroughly coated in the sauce.

Remove the skillet from the heat and gently fold in the sour cream. Stir until the sauce is velvety and fully incorporated.