Everything above-ground! :-) The stems are pretty succulent. I usually break off a big chunk of it (have to be careful not to uproot it), rinse it off, and chop it up finely enough that there aren't long pieces of stem.

Later in the year as it goes to seed the stems become tougher and the whole plant becomes drier, so it's not particularly good to eat. But this time of year it's very tender.