Dry Lake View is the perfect spot to start this hike, as it is located in the saddle between both peaks. First hike to Dry Lake View and drop your overnight pack. I have hiked all routes suggested below.
I recommend peaking Charlton first. Hike directly north out of Dry Lake View Campsite and ascend the ridge. Soon you will arrive at Little Charlton. This should be fairly easy after your haul to Dry Lake View Campsite. Pass little Charlton and continue on the ridge in a N/NW direction. There will be a decline, and then you will ascend up to Charlton Peak. The views are best at the very North end of the peak. Descend just a little bit for the best views. Great views of the South Fork Drainage. Return to Dry Lake View Campsite. On the return trip to Dry Lake View Campsite be sure to visually survey your route up Jepson Peak. Note the location of the routes described below, including the Dollar Lake Trail.
The most direct route to Jepson Peak is to ascend directly up the NW Face. This route is very steep and tough. Stay out of Jepson Bowl. As long as trees are to the left (east) of you then you will be out of the Jepson Bowl. If there are no trees to the left of you then you are too far east and risk heading into the Jepson Bowl. Head west. The first peak you will see is a false summit. Steam past it to the true summit of Jepson Peak. There will be a registry on the true Summit.
The second and easier option is to take the Dollar Lake Trail southwest out of Dry Lake View. This is my recommended route. Ascend past the tree line. Soon you will come to a spectacular viewpoint where you will get your first view of Mill Creek. This specific view point is on my short list of best view points in the entire wilderness. There is a very large and prominent rock at this view point. Hop up and take some photos. This is the best view to the west that you will have as it will soon become obscured by the broad East slope of Jepson Peak. Now leave the trail and head East to ascend the East face of Jepson Peak. Though longer than the previous route, it is considerably easier. Again, the first peak you see will be a false summit so chug past it.
To add some variety to your return route, I recommend following the trace trail southeast off the summit of Jepson Peak. It will eventually drop you off right at the Dollar Lake Trail. Well actually a few yards away, but just look to the right (west) and you will easily see the trail. Turn right and head northwest on the Dollar Lake Trail to return back to Dry Lake View Campsite.
Post an update and let us know how it goes!