The underside of the leaf has an unmistakeable mealy or grainy look. Yes, they're edible (I believe both raw in salads and as a cooked vegetable).

It would be helpful to know generally where you live (growing zone if you know that) and when you picked the leaves. Also, even better would be if you could post a photo of the whole plant if you have it growing near you. Besides honeysuckle, it resembles lilac stems in spring to me.

Thanks! Edit - Apparently this is the "Elegant Stinkhorn" with the... interesting common name of "faeces carota" lol. I wonder if that means what I think it means :D

just a guess - an echeveria?