Preheat the oven to 400 degrees F.
Trim the beets and place on a sheet of aluminum foil. Drizzle with olive oil and sprinkle with salt and pepper. Wrap the beets in the foil and bake until tender, about 45 minutes. When cool enough to handle, peel the beets, slice in half lengthwise, and then slice into 1/4-inch-thick half-moons.
For the dressing, heat 3/4 cup of the orange juice and the sugar in a small saucepan over medium-high heat. Simmer until the mixture is reduced to about 3 tablespoons, about 30 minutes. Cool completely.
Whisk the orange juice reduction with the olive oil, the remaining 2 tablespoons orange juice, the goat cheese, champagne vinegar, heavy cream and 1 tablespoon water in a medium bowl. Sprinkle with salt and pepper.
Cut off both ends of the oranges. Carefully cut off the skin and pith, and then slice the oranges in half and then into 1/4-inch half-moons.
Mix together the arugula and onions in a large salad bowl. Divide the salad among 4 plates. Arrange the oranges and beets over each salad and drizzle with the dressing.
If using both golden beets and red beets, wrap them separately so the red beets don't dye the golden beets while they cook.