Violets (Viola) instantly come to mind, they meet your definition of "hearty" and prefer some shade, though they also prefer constant moisture...
English daisy (Bellis perennis) and Chamomile (Matricaria recutita) are another couple of possibilities, but they prefer a location that is more toward full-sun, therefore they may struggle somewhat in "mostly partial shade".
Wild Strawberry (Fragaria vesca) is another option that will tolerate some shade, not sure how edible the leaves are, but they are used in (herbal) teas.
Q. Does the chosen ground cover need to be able to stand up to foot traffic?
Q. Location in the landscape: Full-sun, partial-shade or full-shade?
Q. Water requirements: Able to survive via rainfall only or will irrigation be provided during warm, dry spells?