Butternut (Juglans cinerea)
An early ripening nut in the walnut family. This nut is more oblong and milder tasting than the walnut.
I did not harvest this plant, but the friends that did were told what they had by a native to these mountains. That person claimed that branch lettuce was becoming rare due to over harvesting. It can be eaten raw in a salad, or cooked in bacon fat.