Heat butter in a large pot over medium. Add onions and mushrooms, cook 5 minutes. Transfer to a bowl.
Toss beef with 3 tablespoons flour. Add 1 tablespoon oil to the pot, increasing heat to medium-high. Brown half the beef for 2 minutes. Repeat oil and beef browning with remaining meat. Transfer to the onion bowl.
Reduce heat to medium. Whisk 1/2 can of beef broth, Worcestershire sauce, and mustard in the pot, scraping up brown bits. Add the mixture from the bowl back to the pot along with remaining broth and optional red wine. Cover and simmer on low for 15 minutes.
Uncover and stir in carrots. Cover and cook 45 minutes more.
In a small bowl, stir together 2 tablespoons water and remaining 1 tablespoon flour, along with rosemary, salt, and pepper. Stir into stew and cook 3 minutes until thickened.