Preheat the oven to 350°F/180°C.
Using a paper towel or mister, apply a thin coat of vegetable oil to the inside of a cast iron rectangular baker. Arrange the acorn squash in the pan, cut side up.
In a mixing bowl, combine the shallot, brown rice, ginger, cranberries, raisins and apple pieces. Divide evenly among the squash cups.
In a small bowl, combine the melted butter and vinegar. Pour butter mixture over the fruit mixture and divide evenly among the squash cups.
Place a piece of orange zest on top of each squash cup and sprinkle with a pinch of grated nutmeg.
Cover the pan with aluminum foil and bake for 30 minutes.
Uncover the pan and bake an additional 5 - 10 minutes or until squash is tender when pierced with a paring knife.