Place the beets on a parchment paper-lined baking sheet. Drizzle with olive oil, season with salt and pepper. Bake the beets until tender, about 15-20 minutes. Set aside to cool.
In the meantime, whisk all of the ingredients for the dressing in a bowl. Season with salt and pepper to taste.
Lay the cooled beets on the arugula. Top with onions, pecans, and goat cheese. Lightly dress the salad before serving.