Place the flour on a plate. Dredge the beef cubes in the flour. In a large, heavy saucepan, heat the oil over medium heat. Add the beef and cook, turning as needed, until browned on all sides, about 5 minutes. Remove the beef from the pan with a slotted spoon and set aside. Add the fennel and shallots to the pan over medium heat and saute until softened and lightly golden, 7 to 8 minutes. Add 1/4 teaspoon of the pepper, the thyme sprigs and the bay leaf. Saute for 1 minute.
Return the beef to the pan and add the vegetable stock and the wine, if using. Bring to a boil, then reduce the heat to low, cover and simmer gently until the meat is tender, 40 to 45 minutes. Add the carrots, potatoes, onions and mushrooms. The liquid will not cover the vegetables completely, but more liquid will accumulate as the mushrooms soften. Simmer gently until the vegetables are tender, about 30 minutes longer. Discard the thyme sprigs and bay leaf. Stir in the parsley, the 1/2 teaspoon salt and the remaining 1/2 teaspoon pepper. Ladle into warmed individual bowls and serve immediately.