Note: "Epaulie" is an unofficial name given to a point a half mile SE of the Epaulet Mountain summit that measures 13,530 ft., which is 7 feet higher than Epaulet, making Epaulie the official high point.
From the parking area at Summit Lake, walk south parallel to the road and follow it as it turns SW, then W. Once you've reached the section of road above the broad saddle north of the Epaulet summit, begin hiking directly south over boulder-strewn, tundra terrain to the summit of Epaulet Mountain, gaining about 325 feet in the process. From the summit, walk SE a little over one half mile toward the "Epaulie" summit by losing about 150 feet, then gain the "Epaulie" summit which is about 7 feet higher than Epaulet.
If doing Epaulie by this route, it would make good sense to go ahead and continue another 1.25 mile SE to the Rosalie summit. Then return as you came. See the Rosalie route description for further details. This would be a longer, but still very friendly "family" hike.
Alternate route: For a more "sporting" climb of these two peaks, consider heading out of Denver on HWY285, through Bailey and turning north at Grant on CR62. Drive about 5 miles north to the "Abyss Lake" trailhead. Walk up that trail along Scott Gomer Creek to an elevation of 12,200 ft., where the trail for Abyss Lake turns abruptly from NE to NW. Depart the trail and hike toward the imposing cliffs that ring the east side of this valley. In those cliffs, there's actually a steep couloir that allows passage up to the saddle just north of Epaulet Mountain. From there, finish off the two summits as described in our route descriptions. This would be a very long day hike. It might work best as an overnight backpack. This area around Abyss Lake, Mt. Bierstadt and Mt. Evans sees few visitors, comparatively speaking.