I do not think that word means what you think it means
Saw this sign today and was initially excited by the possibility of a Complete Cookie. And then was deflated to see that "complete" was actually defined by all the things that this cookie is not. I support a vegan, possibly joyless cookie, sure, but this is a tragic misuse of a description. Maybe call it an incomplete cookie...or a cracker with date juice. But don't mislead your reader, you'll only cause resentment and maybe even sorrow. Or hanger.