This is a great summer scramble. The views of Glacier Basin as you climb Cadet are awesome.
From Barlow pass, ride mountain bikes up to the old townsite of Monte Cristo, then follow the hiking trail up to Glacier Basin.
Hike up into Glacier Basin until the basin becomes very wide and flat. Don't try to cross to creek too early. Here you will find the house size boulders that other route descriptions talk about. But more importantly, the creek coming down will spread out enough so you can cross it. In July of a big snow year, it was a challenge to keep our boots dry, especially in the afternoon on the way back down, (the warm weather increased the flow).
In the basin, you will see a dirty brown 200 yards long 10 yards wide gully coming down from Cadet. It is very obvious. In June and maybe even July it will be full of snow. Go right up it or up the rocks to the right of the gully. Go all the way to its end, then traverse left 200' to the bottom of a grey rocky gully.
Climb up this second gully. Watch for rock fall and put on your helmet. Keep the party tightly together. You can avoid the gully by climbing up the brushy ridge to its left, but don't do it in short pants and short sleeves. The gully goes up a couple hundred yards to where it widens and joins up with the ridge on its left. Eventually, you need to cross the ridge on the left on to the wide open slopes, but don't do it until the last minute, it is easier to stay on the right until you cliff out, then join the wide open heather / rocky slopes to the left. The elevation here is approximately 5400' (I did not write it down).
Once on the open slopes, (50 yards wide), go straight up, but generally keep right at any choices.
At about 6300' look up and see the wide dark cliff band which is at exactly 6500'. This is the crux move of the whole trip and is where lots of people screw up. If you had been keeping right, then right above you is a good looking notch up through the cliff band. Don't take it. Look to the left 100 yards and see a blocky gendarme sticking up on cliff band. It is not very visible from 6300', but is more prominent the higher you get. 75 yards more yards to the left is a deep scary looking gully. The climbing route is the ridge inches to the right of the big gully. If you are down at 6300' looking up at the cliff band, traverse toward the gully and you will see the route. There is a good class 3 move here that will make your hiking friends nervous.
Once you get up above the cliff band the route is straight forward and you can find it without any advice, but getting back to this point is not super easy. The cliff band and scary gully are not visible from above, so pay close attention to how to get back to right here, especially if you are in the clouds.
Final note about the dirty brown gully at the bottom of the scramble route: In the afternoon, if it is full of snow, you can slide down it, but at the bottom 100 feet stay to the edge not the middle. Normally on snow slopes the middle is better than the edges, however this is an exception. Water runs down underneath forming a big ice cave. The middle is what gets thin and the sides stay thick. At the end, climb down and peer up into it. The mid-July day that we went, the last 50 feet of the 300 foot long snow filled gully was under-cut.
The day we went, from down in the valley, we could see a few bands of snow below the 6500' cliff band. We were able to go around those. There was no snow in the flat part of the basin. The dirty brown gully had snow, but we were able to cross above it on the way up.
We had less snow than on the picture that I linked to this description, (that was not my photo).
If your conditions seem similar, you could leave your axes in the basin.