Bring stock, potatoes, carrots, parsnips, and turnips to a boil in a large saucepan. Reduce heat, and simmer until just tender, about 6 minutes. Drain, reserving 1/2 cup liquid; set aside.
Meanwhile, heat oil in a large non-stick skillet over medium heat. Add onion; cook, stirring occasionally, until softened, about 6 minutes. Add vegetables and the reserved 1/2 cup cooking liquid. Cook, stirring occasionally, until vegetables are browned, about 25 minutes. Stir in corned beef and mustard. To serve, top with eggs, and season with pepper.