A path of use trail leading into the gulch on the north side of the highway leaves from the Tanners Flat Avalanche Area sign at 4.3 miles up Little Cottonwood Canyon or 0.1 miles up from the turnout to Tanners Flat Campground.
Warning: Do this route only between early May and late June or early July. This is one of the worst avalanche chutes in the country, so don't attempt it in winter. Summer and fall are also unpleasant and not very safe because of loose rock and scree. When it's the right season, this is one of the finest climbs in the Rockies.
From the trailhead, climb up the gulch with an ice axe until it forks at about 8,500 feet. A more difficult-to-navigate cliff-band blocks easy progress up the left fork. The right branch leads to Dromedary and the left fork more directly to the Dromedary/Sunrise saddle. Take a left at the major branch in the gulch in the gulch and scramble up to the saddle between Sunrise Peak (O' Sullivan Peak) and Dromedary Peak. However, the route opens up again at about 8,800 feet. It is feasible to contour back over to the left fork once the cliffband has been bypassed anywhere between 8,700-9,400 feet, and you can traverse all three summits. From there scramble over the summit of Sunrise and continue west to the Broads Fork Saddle, then continue west along the ridge to the summit of Twins. There is much scrambling along the way. The Tanners Gulch route is for tough and experienced climbers only. The elevation gain to the Twins is about 4200 feet including the drop to the Broads Fork Saddle.
Alternate route: Take a right (east) at the major branch of the gulch and the route leads up to Dromadary Peak. From Dromadary, follow the ridge west over Sunrise (!) and over to the saddle between Sunrise and Twins. If you have the energy, climb Twins and return to the saddle. Return to Tanners Gulch via a glissade down the west branch and down Tanners. This is a long all-day adventure.
Tanners Gulch is the prominent snow gully.
Ice axe; crampons may come in handy too.