Heat a large skillet or Dutch oven over medium-high. Add the ground beef and break it up with a spoon. Cook until nicely browned, about 7 to 10 minutes. Drain off excess grease and return the meat to the pan.

Turn the heat to medium. Sprinkle in the salt, black pepper, garlic powder, and onion powder. Stir to coat the beef and bloom the spices.

Add the butter to the pan and let it melt. Once melted, sprinkle in the flour and whisk constantly for 1 to 2 minutes to form a light roux.

Slowly pour in the beef broth while whisking so the mixture stays smooth. Bring to a gentle simmer and cook for 1 to 2 minutes to thicken slightly.

Whisk in the milk. Continue stirring until the sauce thickens and becomes creamy, about 5 to 7 minutes. Taste and adjust seasoning.

Meanwhile, bring a pot of salted water to a boil and cook the egg noodles until al dente according to package directions. Drain well.

Add the drained noodles to the skillet and toss to coat them in the stroganoff sauce. Remove from heat and gently stir in the sour cream until combined. Serve immediately.