Preheat the oven to 350 degrees F.
Roast the beet until tender, about 45 minutes depending on size. Let cool, then peel. Slice into wedges and set aside.
Blanch the haricots verts in well-salted boiling water until al dente, 3 to 5 minutes. Immediately shock in an ice water bath.
Drain the haricots verts and transfer to a bowl. Add the lemon juice and olive oil, and season with salt and pepper; toss to coat.
Lay the prosciutto slices on a plate and top with the haricots verts.
In the same bowl toss the beets with a little salt and pepper, then place on top of the haricots verts.
Crumble the goat cheese over the top. Garnish with the sprouts.