Coat the beef with the flour.
Heat the butter in a 12-inch skillet over medium-high heat. Add the beef and cook until it's well browned on all sides. Remove the beef from the skillet. Pour off any fat.
Add the shallots to the skillet. Cook for 10 minutes or until they're tender. Stir in the stock, tomatoes, vinegar and sugar and heat to a boil. Return the beef to the skillet. Reduce the heat to low. Cover and cook for 1 1/2 hours.
Add the carrots and mushrooms to the skillet. Cook for 30 minutes or until the beef is fork-tender and the vegetables are tender. Remove the beef and vegetables from the skillet and keep warm.
Increase the heat to high. Cook for 10 minutes or until the stock mixture is thickened. Return the beef and vegetables to the skillet. Season as desired. Sprinkle with the parsley and lemon zest.