Sift the flour, salt and pepper onto a plate. Add the beef in two batches and toss it well to coat thoroughly. Heat half the dripping or olive oil in a large saucepan until sizzling; add half the beef cubes and cook over medium heat, turning frequently, until evenly browned. Remove the meat from the saucepan with a slotted spoon and put on a plate. Brown the rest of the meat in the dripping or oil that is left in the saucepan, then add to the first batch.
Heat the remaining dripping or oil in the saucepan, add the carrots and onions and the diced turnip and cook, stirring frequently, until the onions have softened. Return the browned meat to the saucepan with any remaining flour and cook for 1 minute. Gradually stir in the beef stock, add the bay leaf and thyme and bring to the boil, stirring continuously. Reduce the heat to very low, and simmer the stew, covered, for 2 hours, stirring occasionally.
To make the dumplings, sift the flour into a bowl and mix in the suet, sausage meat and chopped parsley. Season lightly with salt and black pepper, then add the cold water to the mixture to make a soft, slightly sticky dough.
With floured hands, divide the dough into eight equal portions and roll each lightly into a ball. Add the dumplings to the gently simmering stew, spacing them well apart. Cover and cook the stew for a further 30 minutes, or until the dumplings have puffed up and are cooked through. Remove the bay leaf and thyme and serve immediately.