Season the beef with the salt and pepper and brown it in two batches in the oil, 5 to 6 minutes per batch.
Add the beef to a 6-quart slow cooker with the onion, mushrooms and garlic.
Whisk the broth, mustard, Worcestershire and thyme and pour it into the cooker.
Cover and cook on low until the beef is tender, 6 1/2 to 7 hours.
Whisk the cornstarch with the cold water, stir it into the cooker and cook on high until the gravy thickens, about 10 minutes.
Turn off the cooker, let the bubbling stop and fold in the sour cream until no white streaks remain.
Boil the egg noodles according to their package until tender, drain them and serve the stroganoff over the hot noodles.