Preheat the oven to 200 C.
Rub the beetroot with the oil and some salt, then loosely wrap together in foil with the thyme sprigs. Bake for about 1 hour, or until a sharp knife can be pushed through a beetroot without much resistance.
While the beetroot is still warm, rub off the skins, then cut into rough wedges. Place in a large bowl and pour the dressing over the top. Toss well to coat.
Tear the radicchio wedges into uneven pieces and add to the beetroot.
Add the fennel to the bowl, along with the picked parsley leaves. Season with salt and pepper and toss well to coat.
