Preheat the oven to 400°. Set the beets in a small baking dish, add 1 cup of hot water and cover with foil. Bake for about 45 minutes, until the beets are tender when pierced with a knife. Drain and let stand until cool enough to handle. Using a paper towel, rub the skins off the beets. Cut the beets into 1/2-inch dice.
In a small skillet, toast the pine nuts over moderate heat until golden, about 4 minutes. Transfer the pine nuts to a small bowl.
In a large bowl, gently toss the beets with the scallions, olive oil, vinegar and 1 tablespoon each of the dill and mint. Season with salt and pepper. Add the arugula and toss to coat. Transfer the salad to plates. Spoon 2 tablespoons of the ricotta over each salad and season the ricotta with pepper. Sprinkle with the pine nuts and the remaining 1 teaspoon each of dill and mint. Serve at once.
The beets can be made through step 1 up to 2 days in advance.