We did this route with extreme hot temperatures and bad ice.
You start at the valley Klein Scheidegg and walk up to the Guggi hutte, 2791 m. This is a small nice cabin without a guardian in the pre-summer time. The last section -traverse on slab also the traverse direction Monch- can be slippery in wet or icy conditions. If you arrive, start with exploring the rest of the route in daylight, direction Monch.
Start with this route in the period with good conditions, april-june.
Next day, start early and follow the cairns you made the day before marking the way. Climb over slab rock, make a long horizontal traverse to the left (N).
Up to the Monchplateau 3112 m. Follow the ridge side to the firnfield up. Keep left.
Go over the bergschrund and start iceclimbing.
Start at the left side from the icewall, it's going straight up, 80-60 degreeds. Only for one pitch followed by two pitches, than you will find better ice and less steep (50 degreeds) conditions. Climb up for another more pitches in the wall and than you can go:
1)to the right were you meet the rockridge and follow it to the left.
2)or you can go more up left in the wall to the pre-top.
Here you scramble a little, and walk over a very small and steep iceridge(SW) and follow the terrain (NE) to the top. Go down the normal route. Monschjochhutte 3650 m. is a place to sleep.
Two technical icegear, crampons, rope (50 m is fine) some icescrews, nuts, food for the night at the cabin. You will find there mattress, water and blankets, kitchen tools, emergency phone and wood-firestove. Pay for the night!! Keep it clean!!