I realize this post was a while ago, but I just saw it today. Anyway, if you're still looking for answers, we had a similar issue, although our tree was surrounded by grass. The roots came up just like your photo, making mowing a real headache.

Last fall we had a bunch of landscaping done and the solution for this problem was to add a couple of inches of top soil and plant ground cover in that. We had a whole bunch of vinca that we needed to move from another bed so that's what we put in. It seems to be settling in nicely.

From what we learned at that time, the key point is to cover the roots by no more than 2 inches of soil but that adding that amount should be okay. You might want to verify that advice yourself, but so far (10 months later) tree and vinca seem to be doing fine.

Covering a tree with more dirt is dangerous. Don't surround the trunk with dirt! That would make it rot.

Moss likes shallow dirt. Clover makes fertilizer, so there would be an added benefit to planting that.