A nice little ice climb not in the BAC guidebook. Just to the right of the Albinini-Gabbarou. The first pitch is usually done as a running belay over easier ice past a pretty sizable bergshrund. The final pitch is thin (at least in 2006) and a little bit mixed and delicate. The rest is all chop-chop with the axes.
TVMountain.com has a nice photo and video here - http://www.tvmountain.com/topo/mixte/lafaille.htm
Rappel down the route using handy fixed anchors. TVMountain says you can continue to the summit, but nobody ever does.
Like the Albinini-Gabarrou, you can access in winter/spring by the Aiguille du Midi first bin. Down the arete, a short ski past the Rongon and bearing right, then a short (100mH?) ski tour up to the start of the climb.
When finished, rap down the route and then ski down the Vallee Blanche all the way to Chamonix or halfway and using the Montenvers train.
Alternately, as a non-ski venture, you could stay the night at the Cosmiques or Abri Simond refuges and do the trip round-trip from there and take the Midi cablecar back down.
Do not underestimate how long it can take to wade through deep snow without skis, even if you have snowshoes.
2x60m ropes. Technical ice climbing gear (2xaxes, crampons, etc.)