Preheat oven to 375°.
Melt butter in a 9-inch cast-iron skillet; sprinkle evenly with brown sugar. Drain pineapple slices over a bowl, reserving 1/2 cup juice. Place 1 pineapple ring in center of skillet. Cut remaining pineapple rings in half; arrange around center pineapple ring. Sprinkle evenly with coconut. Set aside.
Lightly spoon flour into a dry measuring cup, and level with a knife. Combine flour and next 5 ingredients (flour through salt) in a large bowl. Combine reserved juice, banana, oil, and egg, stirring with a whisk. Add pineapple juice mixture to flour mixture, stirring until combined. Pour flour mixture over coconut. Bake at 375° for 30 minutes or until a wooden pick inserted in center comes out clean. Invert onto a wire rack. Serve warm or at room temperature.