Add the lamb, onion, carrots, garlic, paprika, beef broth, crushed tomatoes, salt, and pepper to the slow cooker. Stir until the meat and vegetables are evenly coated with the spices and liquid.
Cover and cook on low for 8 hours, until the lamb is fork-tender and the broth has thickened slightly.
About 15 minutes before serving, cook the egg noodles in a pot of boiling water according to the package directions, then drain.
Divide the noodles among four bowls. Ladle the lamb stew over the noodles.
Top each bowl with a generous spoonful of sour cream and a sprinkle of parsley before serving.