Brown the boneless beef stew meat in the butter in a skillet over medium-high heat.
While the beef is browning, combine the beef broth, mushroom stems and pieces with juice, and dry onion soup mix in a crock pot.
Transfer the browned beef to the crock pot and stir to combine.
Cover and cook on low for 7 to 8 hours.
Mix the flour and water together in a small bowl until smooth.
Stir the flour mixture into the crock pot and turn the heat to high.
Cook for about 30 minutes until the sauce thickens.
Cook the egg noodles according to package directions.
Turn off the heat and stir in the sour cream until fully combined.
Serve the beef mixture over the cooked egg noodles.