Wash the beets thoroughly to remove any dirt, then trim off the greens and root ends. Peel beets.
Toss the beets with 1 tablespoon of olive oil, 1 teaspoon salt and ½ teaspoon pepper and coat well.
Wrap the beets in aluminum foil and roast in the oven for 35 minutes. When done, you should be able to easily insert a fork into the beets and remove it cleanly. If not, continue roasting for a few more minutes until a fork comes out easily. Carefully unwrap the foil from the beets and allow to cool.
Slice beets into ½-inch-thick wedges, and, if large, cut in half crosswise. Set aside.
Make the dressing & salad
In a large bowl, whisk together the olive oil, red wine vinegar, minced shallot and Dijon mustard. Add salt and ground pepper to taste.
Place beet slices and arugula into bowl with the dressing, gently toss to coat.
Transfer to a serving dish, sprinkle salad with feta cheese and pistachios, and serve.