For the creamsicle cake: Preheat a grill to 350 degrees F.
In a bowl, sift together the flour, baking powder, salt and nutmeg. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and granulated sugar together until light and fluffy, stopping occasionally to scrape down the bowl.
One at a time, add the eggs and egg yolk, beating after each addition until incorporated and scraping down the bowl occasionally. Once all the eggs are incorporated, alternate adding the flour mixture and the buttermilk, mixing slowly. Fold the batter a few times with a rubber spatula to make sure everything is evenly distributed and the batter is smooth.
Spoon the batter into the hollowed out orange shells, filling them halfway.
Loosely wrap each orange in foil and set upright on the grill. Cover the grill and bake for about 40 minutes, until the cakes spring back when poked. Remove from the grill, unwrap and let cool completely.
For the cream cheese frosting: In a large bowl, beat together the butter and cream cheese with an electric mixer. On low speed, add the confectioners' sugar 1 cup at a time; beat until smooth and creamy. Beat in the vanilla.
Spread the cooled cakes with a generous dollop of cream cheese frosting.
You may have some excess batter depending on the size of your oranges. If you do, you can make additional oranges or bake off the extra batter in muffin tins in the oven. For oven baking, place the foil-wrapped oranges on a sheet tray and bake at 350 degrees F for 25 to 30 minutes.