Preheat the oven to 400 degrees F.
Place the potatoes on a baking sheet and bake until tender, about 1 hour. Remove from the oven and let rest until just cool enough to handle. Lower the oven to 350 degrees F.
Make the orange cups by cutting the oranges in half and scooping out the pulp, leaving only the shell. Set aside.
While still somewhat hot, peel the potatoes and place in a large bowl. Discard the skins and tough, stringy fibers. Add the butter, and with an electric mixer, beat out the lumps.
Add the sugar, eggs, orange juice, heavy cream, and brandy, and mix until smooth. Add the cinnamon, nutmeg, and salt, and mix well. Re-season, to taste.
Spoon the sweet potato mixture into the orange cups, mounding and smoothing the top. Bake until puffed and slightly golden, about 20 minutes.