Approach

Park the car near the barrier in Val Veny, Italy and walk up the road to the Lac Combal. Take the sign-posted path on the right, which goes up onto the grassy moraine on the true right hand side of the Miage Glacier.  This becomes quite thin, (an alternative path comes up from the left,) before you drop down to the right onto the glacier rubble.  Go up this in the middle, faint path with some cairns.  Eventually, just before a rock buttress, the rubble gives way to ice (or snow early in the season).  Go up this before turning right to gain a path with cables etc, which leads to a band of rock and the hut. About 4h30.

Route

Glacier du Dôme & Col des Aiguilles Grises
From the hut, follow a short faint path to get onto the Dôme glacier.
The route up the glacier is very complex due to the numerous crevasses.  Go up the true right bank at first then traverse to reach the central branch of the glacier, which you follow as best as you can to reach the ridge at the col Aiguilles Grises (or higher depending on the conditions.)

Aiguilles Grises Ridge & Dôme du Goûter
Go up this pleasant snowy ridge, (with some easy rock sections.)  At about 4000m you reach the Piton des Italiens (4002m). Follow the ridge to the Dôme du Goûter, initially narrow to 4150m then broader.
Continue until almost the summit of the and then down to the Col of the Dôme du Goûter  and the normal route from the Gouter hut

Arête des Bosses
Go up to the Vallot hut and then follow the Bosses ridge to the summit.

Descent

Various options :
•    By the Gouter Hut
•    By the Grands Mulets Hut
•    By the 3 Monts to the Aig. du Midi
•    By the ascension route, not recommended, unless the condition of the glacier was very favourable, (or on skis).   The risks involved if conditions are not ideal greatly outweigh the hassle of having to recuperate a car from Val Veny.
•    By the Bionnassay glacier on skis,  on the very rare days when the conditions are good.  From the Piton des Italiens, Go down the ridge for a bit to reach a nice north facing slope which gives acces to the Bionnassay glacier. Descend this, keeping to the centre until a large crevasse at about 3400m, (often impossible to cross!) go to the true left bank.  Lower down at about 3100m use the true right bank to get to the Miage glacier which gives easy skiing down to the moraine (2100m) , from where a path leads back to the car