Prepare a medium hot grill with coals to one side.
Lightly brush the pineapple rings with some butter and grill them long enough to get grill marks, then remove the rings.
In a 12-inch cast-iron skillet, combine the brown sugar, cream, cinnamon and butter. Cook until sugar dissolves and bubbles. Remove the skillet from the heat and lay the pineapple rings across the bottom of the pan.
In a large bowl, mix together flour, baking powder, baking soda and salt. In a separate bowl, mix buttermilk, eggs, rum extract and vanilla. With an electric mixer on medium speed, cream the butter and sugar until smooth. Add the flour mixture and blend. Pour and spread the batter over the pineapples.
Place the cake on the grill over indirect heat and cook for 45 minutes. Grill temperature should be approximately 350 F.
Remove from grill, let stand for five minutes and serve.