Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Brush the pineapple rings with the melted butter. Brush the cooking grates clean. Grill the pineapple over direct medium heat, with the lid open, until nicely marked, 4 to 6 minutes, turning once. Remove from the grill and let cool. Leave one pineapple ring whole and cut the others into halves.
In a 12-inch cast-iron skillet over direct medium heat, combine the brown sugar, cream, cinnamon, and any melted butter remaining from brushing the pineapple slices. Cook until the sugar has melted and the liquid starts to bubble around the outer edge, about 2 minutes. Remove the skillet from the heat and place on a sheet pan. Place the whole pineapple ring in the center of the skillet, and then arrange the pineapple halves around it. Set aside.
In a large bowl mix the flour, baking powder, salt, and baking soda. In a small bowl whisk the buttermilk, eggs, and vanilla.
In a large bowl using an electric mixer, cream the butter and sugar on medium-high speed until light and fluffy, 2 to 4 minutes. With the mixer on low, add the buttermilk mixture and then gradually add the flour mixture. Blend until smooth, scraping down the sides as necessary. Using a rubber spatula, spread the batter evenly over the pineapple slices in the skillet.
Bake the cake over indirect medium heat, keeping the temperature of the grill as close to 350°F as possible, with the lid closed, until the top is golden brown and a skewer inserted into the center comes out clean, 40 to 50 minutes. Wearing barbecue mitts, remove the cake from the grill and let cool at room temperature for about 10 minutes.
Before removing the cake from the skillet, run a paring knife around the edge to loosen it. Place a serving platter, large enough to hold the cake, over the top of the skillet. Wearing barbecue mitts, carefully invert the skillet and platter at the same time, and then slowly remove the skillet. Replace any pineapple that has stuck to the bottom of the skillet. Let the cake cool briefly before slicing into wedges and serving. The cake is best served warm or at room temperature the day it is made.