Adjust an oven rack to the middle position and heat the oven to 400 degrees. Toss together the beets, cumin seeds, 1/2 teaspoon salt, and 1/2 tablespoon olive oil in a large bowl. Wrap each beet separately in aluminum foil and place on a rimmed baking sheet. Cook the beets until soft and easily pierced with a paring knife or skewer, about 1 hour. Once the beets are cool enough to handle, peel them by rubbing them with a paper towel—the skin should slide right off. Cut each beet into 6 or 8 wedges.
Toast the pine nuts in a medium skillet over medium heat, stirring frequently, until light golden, 5 to 6 minutes. Transfer the nuts to a small bowl and set aside.
Process the remaining olive oil, sherry vinegar, balsamic vinegar, mustard, 1/8 teaspoon salt, and a pinch of pepper in a blender until fully emulsified, 20 to 30 seconds. Stir in shallot and adjust the seasoning with salt and pepper. Toss the beets with 1 tablespoon of the vinaigrette in a medium bowl.
Toss the arugula with the remaining vinaigrette in a medium bowl. Divide the arugula equally among chilled salad plates and top with the beets. Sprinkle with the pine nuts and serve immediately.