Cook the beets until tender. It may take a while, so only at the end you can prepare all the other ingredients.
Chop the nuts, and toast them on a skillet. Chop the parsley leaves and mix them with the olive oil, salt and black pepper. Peel the beets and cut them into "coins" and toss them with the olive oil mixture, until the beets are coated with it. Arrange the arugula on a serving plate, top it with the beet coins. Crumble the blue cheese with your fingers and put it on the beets and the arugula. Spread the walnuts and drizzle the balsamic vinegar on top. Serve immediately.