The rather lesser-known route follows a marked hiking trail along Schafberg, first reaching Rosseck. At the summit cross, there is a lovely resting spot with a breathtaking view. From there, the trail continues on to Mugel and the mountain shelter.
If you get hungry during the descent, you can take the turnoff to the "Lanner-Huab'n" just after the second gate (winter parking area). (This turnoff is hard to miss due to the clear signs.)
Tourist Office Hochsteiermark