Brown beef and onion in a 6-quart Dutch oven over medium-high heat for 8 minutes, breaking up the beef and cooking it to 160°F. Drain excess fat, leaving about 1 tablespoon.
Add mushrooms and cook for 6 minutes until their liquid has mostly evaporated. Stir in garlic for 30 seconds.
Add broth, Worcestershire, mustard, salt and pepper and bring to a boil. Stir in egg noodles and reduce to a lively uncovered simmer.
Cook for 8 to 10 minutes, stirring gently and adding reserved water in small amounts if the noodles are not tender before the liquid reduces to a coating sauce.
Remove from the heat and wait for bubbling to stop. Mix sour cream with 1/4 cup hot sauce from the pot in a small bowl, then fold it back into the noodles.
Rest for 2 minutes and divide among 4 bowls; keep the finished sour-cream sauce off the boil.