1Heat butter in a large pot over medium heat. Add onion and mushrooms and cook 5 minutes. Transfer to a bowl.
2Meanwhile, toss beef with 3 tablespoons of the flour. Add 1 tablespoon of the oil to the pot and increase heat to mediumhigh. Add half the beef and cook 2 minutes, browning on all sides. Transfer to bowl with onions and mushrooms. Add remaining tablespoon oil and second half of beef to pot. Cook 2 minutes, browning on all sides. Transfer to bowl; reduce heat to medium.
3Add 3/4 cup of the beef broth to the pot. Whisk in Worcestershire and mustard, scraping up any brown bits on bottom of the pan. Add mixture from bowl back to the pot along with the remaining beef broth. Cover and simmer on low for 15 minutes.
4Uncover and stir in carrots. Cover and cook an additional 45 minutes.
5In small bowl, stir together 2 tablespoons water, the remaining tablespoon flour, rosemary, salt and pepper. Stir into stew and cook 3 minutes, until thickened. Serve with noodles, if desired.noodles, if desired.