Place flour in a recloseable food storage bag; season flour with salt and pepper as desired. Add beef to bag and seal. Shake bag to coat beef. Remove beef shaking off excess flour.
In large skillet with cover, heat oil over medium-high heat. Add beef, onions and garlic. Sauté until beef is browned on all sides (about 3-5 minutes).
Pour in wine or ½ cup broth and deglaze pan by scraping all bits off bottom of pan. Add in beef broth; bring to a boil. Reduce heat; cover and simmer 1½-2 hours or until beef is very tender.
Stir in mushrooms, egg noodles and dill. Cook, uncovered, until noodles are tender (about 10-12 minutes), stirring frequently.
Remove from heat and stir in sour cream. Salt and pepper to taste.