Place the beef stew meat, mushrooms, onion, and garlic in the slow cooker. Add the beef broth, Worcestershire sauce, paprika, salt, and black pepper. Stir to combine.
Cover and cook on low for 7 to 8 hours until the beef is tender.
In the last 30 minutes, whisk the flour with a few tablespoons of the cooking liquid in a small bowl until smooth. Stir the mixture back into the slow cooker to thicken the sauce.
Turn off the heat and stir in the sour cream until fully blended.
While the sauce thickens, cook the egg noodles in a large pot of boiling water according to package directions. Drain and return them to the pot.
Add the butter to the hot noodles and toss until the butter melts and coats them evenly.
Spoon the beef and sauce over the buttered noodles. Sprinkle with chopped fresh parsley before serving.