In a large resealable plastic bag, combine flour, salt, and pepper. Add beef, seal bag, and shake to coat.
In a large Dutch oven, heat 2 tablespoons butter over medium-high heat. Add half of beef, and cook for 5 to 6 minutes or until browned. Remove from pan. Add remaining 2 tablespoons butter to pan, and cook remaining beef for 5 to 6 minutes or until browned. Return all beef to pan. Stir in mushrooms, onion, and garlic, and cook, stirring frequently, for 5 minutes. Add broth, Worcestershire, and thyme sprigs. Bring to a boil over medium-high heat; reduce heat, and simmer for 1 hour or until beef is tender. Add egg noodles, and cook, stirring occasionally, for 8 minutes or until pasta is tender.
In a small bowl, whisk together sour cream and mustard. Add to soup, whisking until combined. Remove thyme sprigs, and serve immediately.