Boil the egg noodles in salted water according to the package directions; drain and set aside. If desired, toss with some butter or olive oil to keep the noodles from sticking together.
While the noodles are cooking, start making the rest of the dish. Melt 3 tablespoons of the butter in a large skillet over medium heat. Add the mushrooms and onions and cook until tender, about 5 minutes. Remove the mushrooms and onions from the skillet to a bowl or plate.
Melt the remaining 1 tablespoon of butter in the same skillet and add the sliced beef. Cook, stirring occasionally, until the beef is lightly browned.
Add 2 cups of the beef broth, the ketchup, garlic, and salt to the skillet; stir to combine, scraping up any browned bits off the bottom of the pan. Bring to a boil, reduce the heat, and simmer, covered, for 15 minutes.
In a small bowl, combine the remaining ½ cup beef broth and the flour until smooth. Stir the flour mixture into the beef mixture in the pan.
Return the mushrooms and onions back to the pan; stir to combine. Bring to a gentle boil and boil, stirring occasionally, for 1 minute or until the sauce has thickened.
Remove the skillet from the heat and stir in the sour cream. Note: This is to prevent the sauce from separating. If you add the sour cream while the sauce is boiling, it may separate.
Taste and adjust the seasoning, if needed. Serve over egg noodles. Sprinkle with chopped fresh parsley, if desired.