I went back and looked at the original string, Jennifer--I remember the discussion! So is your tree peony in the ground now? I assume you moved it from the pot last fall? And did you make sure the roots were several inches deep when you planted it? The thick, woody part of the root in the picture from last year is the herbaceous nurse root that the tree peony was grafted on to. You can see the beginnings of tree peony roots in that pic, too--actually looked pretty good to me! The herbaceous root will eventually rot off and will be replaced completely with the tree peony roots, you just have to keep the herbaceous part buried deep enough that it can't sprout on you.
Have you seen any growth from the woody stem of you tree? That would be a good thing.
