Bring a medium pot of salted water to a boil and cook the egg noodles according to package directions until just tender. Drain and return them to the pot. Stir in 2 tablespoons of the butter until the noodles are coated. Cover to keep warm.

Heat a large skillet over medium heat. Add the ground beef and cook, breaking it up with a spoon, until browned and no longer pink. Drain excess fat if needed and set the beef aside on a plate.

In the same skillet, melt the remaining 1 tablespoon of butter. Add the onion and mushrooms and cook for 5 to 6 minutes until the vegetables soften and the mushrooms release their liquid. Stir in the garlic and cook for 1 minute more.

Sprinkle the flour over the vegetables and stir for 1 minute to form a light roux. Slowly pour in the beef broth while stirring to avoid lumps. Add the paprika, salt, and pepper. Bring the mixture to a gentle simmer and cook for 3 to 4 minutes until slightly thickened.

Return the cooked ground beef to the skillet and stir to combine. Remove the skillet from the heat and let it cool for 1 minute. Stir in the sour cream until the sauce is smooth and creamy.

Divide the buttered egg noodles among four plates. Spoon the beef stroganoff over the noodles and sprinkle with fresh parsley before serving.