Trim the meat of all fat and cut into 1 1/2-in. cubes. Heat the oil in a pressure cooker until very hot and almost smoking. Add beef cubes and cook over high heat, stirring often, until browned on all sides.
Add garlic, onion and mushrooms; stir. Sprinkle with the flour and stir to coat evenly. Add the wine, tomatoes, olives, thyme, bay leaf, cayenne and saffron. Bring to a boil, stirring.
Cover and add the pressure regulator. Reduce the heat and cook according to the manufacturer's instructions, 20-25 min. Uncover as directed. Pour the beef into a serving dish and sprinkle with the chopped parsley if desired. Serves 6 to 8.