There are two things I love about
skiing in Verbier, the first is the amount of blue sky days Verbier has compared to other resorts, and secondly, that the best skiing is easily accessible and you don't have to dress like Rambo and go ski touring for miles just to enjoy it!
In terms of intermediates, the Attelas and surrounding slopes are awesome, and there are always the moguls to the side if you want to challenge one's self that little bit more (at your own risk of course). But for advanced skiers it gets even better. If you really want to be challenged in Verbier you have limitless potential, Mont Gele, or
off-piste the back of Mont Fort (with a guide of course), we could go on, but for myself personally, nothing quite beats Tortin. Verbier's Tortin many moons ago was a black run but now is marked in yellow as an off-piste itinerary run. There are two entrants into it, but I think the best route for scenery, the varied skiing, and challenge is from the Mont Fort side. In fact, if you are a competent skier, I would suggest you start at the top of Mont Fort with the moguls, take a right at the bottom, and then ski all the way down to the bottom. Most advanced intermediates will be comfortable on Tortin, provided the snow is good, but if in doubt, and as it is an itinerary route, don't take chances as sections whilst not horrendous, are nevertheless steep.