Drain the canned pineapple, reserving ½ cup of the juice. Lay the pineapple slices (you should have 10 slices) and the maraschino cherries on a layer of paper towel and pat them dry with another paper towel. Cut 3 of the pineapple slices in half.
Whisk together the gluten-free flour, baking powder, baking soda and salt in a large mixing bowl.
In a medium mixing bowl whisk together the egg yolks, granulated sugar, reserved ½ cup of pineapple juice and vanilla until smooth. Add this mixture to the dry ingredients and combine well.
With an electric mixer, beat the egg whites until stiff but not dry. Fold the egg whites into the batter, combining well.
In a 10-inch cast iron skillet, melt the butter over medium heat. When melted, carefully swirl the pan so that the butter coats the sides of the pan. Add the brown sugar and cook, stirring, until the sugar has melted into the butter and is lump free, about 1 minute.
Let the sugar mixture cool very slightly then lay in the pineapple slices carefully so you do not burn yourself. Start with the center, put one whole pineapple slice in the center then arrange the other six whole slices around it. Place the halve slices in the spaces between the whole slices around the outer edge, the curved side facing toward the center. Place a whole maraschino cherry in the center of each of the whole pineapple slices.
Pour the batter over the pineapples and cherries and bake for 40-45 minutes or until golden brown and a toothpick inserted in the center comes out clean.
Let the cake cool for 2 minutes, run a knife around the outer edge, then invert on a serving platter and let it finish cooling. Make sure you do not let the cake cool too long before inverting or the caramel will harden and the pineapple slices will stick to the bottom of the pan.